Class 12 • Physics

Magnetism and Matter

Chapter-5

302 Questions

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Showing 302 of 302 questions

EasyJEE Mains2014

An example of a perfect diamagnet is a superconductor. This implies that when a superconductor is put in a magnetic field of intensity B, the magnetic field Bs inside the superconductor will be such that :

Options:

A) Bs = $-$ B

B) Bs = 0

C) Bs = B

D) Bs < B but Bs $ \ne $ 0

MediumJEE Mains2026

A long cylindrical conductor with large cross section carries an electric current distributed uniformly over its cross-section. Magnetic field due to this current is:A. maximum at either ends of the conductor and minimum at the midpointB. maximum at the axis of the conductorC. minimum at the surface of the conductorD. minimum at the axis of the conductorE. same at all points in the cross-section of the conductorChoose the correct answer from the options given below:

Options:

A) B, C Only

B) E Only

C) A, D Only

D) D Only

EasyJEE Mains2026

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Consider a ferromagnetic material : Assertion (A) : The individual atoms in a ferromagnetic material possess a magnetic dipole moment and interact with one another in such a way that they spontaneously align themselves forming domains. Reason (R) : At high enough temperature, the domain structure of ferromagnetic material disintegrates. Thus, magnetization will disappear at high enough temperature known as Curie temperature. In the light of the above statements, choose the correct answer from the options given below :

Options:

A) (A) is true but (R) is false

B) Both (A) and (R) are true and (R) is the correct explanation of (A)

C) (A) is false but (R) is true

D) Both (A) and (R) are true but (R) is not the correct explanation of (A)

EasyJEE Mains2026

The magnetic field at the centre of a current carrying circular loop of radius R is 16 \mu \mathrm{~T}. The magnetic field at a distance x=\sqrt{3} R on its axis from the centre is \_\_\_\_ \mu \mathrm{T}.

Options:

A) 8

B) 2

C) 4

D) 2 \sqrt{2}

EasyJEE Mains2025

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Magnetic monopoles do not exist.Reason (R): Magnetic field lines are continuous and form closed loops.In the light of the above statements, choose the most appropriate answer from the options given below:

Options:

A) Both (A) and (R) are correct and (R) is the correct explanation of (A)

B) (A) is not correct but (R) is correct

C) (A) is correct but (R) is not correct

D) Both (A) and (R) are correct but (R) is not the correct explanation of (A)

MediumJEE Mains2026

Three long straight wires carrying current are arranged mutually parallel as shown in the figure. The force experienced by 15 cm length of wire Q is \_\_\_\_ . $ \left(\mu_{\mathrm{o}}=4 \pi \times 10^{-7} \mathrm{~T} . \mathrm{m} / \mathrm{A}\right)

Options:

A) 6 \times 10^{-6} \mathrm{~N} towards P

B) 6 \times 10^{-6} \mathrm{~N} towards R

C) 6 \times 10^{-7} \mathrm{~N} towards P

D) 6 \times 10^{-7} \mathrm{~N} towards R

EasyJEE Mains2025

The percentage increase in magnetic field (B) when space within a current carrying solenoid is filled with magnesium (magnetic susceptibility \chi_{\mathrm{Mg}}=1.2 \times 10^{-5} ) is :

Options:

A) \frac{5}{3} \times 10^{-5} \%

B) \frac{5}{6} \times 10^{-4} \%

C) \frac{5}{6} \times 10^{-5} \%

D) \frac{6}{5} \times 10^{-3} \%

MediumJEE Mains2026

Two identical circular loops P and Q each of radius r are lying in parallel planes such that they have common axis. The current through P and Q are I and 4 I respectively in clockwise direction as seen from O. The net magnetic field at O is :

Options:

A) \frac{\mu_{\mathrm{o}} I}{4 \sqrt{2} r} towards Q

B) \frac{3 \mu_{\mathrm{o}} I}{4 \sqrt{2} r} towards Q

C) \frac{3 \mu_0 I}{4 \sqrt{2} r} towards P

D) \frac{\mu_{\mathrm{o}} I}{4 \sqrt{2} r} towards P

EasyJEE Mains2025

A magnetic dipole experiences a torque of 80 \sqrt{3} \mathrm{~N} \mathrm{~m} when placed in uniform magnetic field in such a way that dipole moment makes angle of 60^{\circ} with magnetic field. The potential energy of the dipole is :

Options:

A) \text { }-40 \sqrt{3} \mathrm{~J}

B) -80 J

C) 80 J

D) -60 J

MediumJEE Mains2026

The current passing through a conducting loop in the form of equilateral triangle of side 4 \sqrt{3} \mathrm{~cm} is 2 A . The magnetic field at its centroid is \alpha \times 10^{-5} \mathrm{~T}. The value of \alpha is \_\_\_\_ . (Given : \mu_{\mathrm{o}}=4 \pi \times 10^{-7} SI units)

Options:

A) 3 \sqrt{3}

B) 2 \sqrt{3}

C) \sqrt{3}

D) \frac{\sqrt{3}}{2}

EasyJEE Mains2025

The relationship between the magnetic susceptibility (x) and the magnetic permeability (\mu) is given by : ( \mu_0 is the permeability of free space and \mu_T is relative permeability)

Options:

A) X=\frac{\mu}{\mu_0}-1

B) X=\frac{\mu_{\mathrm{r}}}{\mu_0}+1

C) \chi=\mu_r+1

D) X=1-\frac{\mu}{\mu_0}

MediumJEE Mains2026

An infinitely long straight wire carrying current I is bent in a planar shape as shown in the diagram. The radius of the circular part is r. The magnetic field at the centre O of the circular loop is :

Options:

A) -\frac{\mu_0}{2\pi} \frac{I}{r} (\pi + 1) \hat{i}

B) -\frac{\mu_0}{2\pi} \frac{I}{r} (\pi - 1) \hat{i}

C) \frac{\mu_0}{2\pi} \frac{I}{r} (\pi + 1) \hat{i}

D) \frac{\mu_0}{2\pi} \frac{I}{r} (\pi - 1) \hat{i}

EasyJEE Mains2025

Match List - I with List - II. List - I List - II (A) Magnetic induction (I) Ampere meter2 (B) Magnetic intensity (II) Weber (C) Magnetic flux (III) Gauss (D) Magnetic moment (IV) Ampere meter Choose the correct answer from the options given below:

Options:

A) (A)-(III), (B)-(IV), (C)-(II), (D)-(I)

B) (A)-(III), (B)-(II), (C)-(I), (D)-(IV)

C) (A)-(III), (B)-(IV), (C)-(I), (D)-(II)

D) (A)-(I), (B)-(II), (C)-(III), (D)-(IV)

MediumJEE Mains2026

A current carrying solenoid is placed vertically and a particle of mass m with charge Q is released from rest. The particle moves along the axis of solenoid. If g is acceleration due to gravity then the acceleration (a) of the charged particle will satisfy :

Options:

A) a>g

B) a=0

C) 0 < a < g

D) a=g

EasyJEE Mains2024

Paramagnetic substances: A. align themselves along the directions of external magnetic field. B. attract strongly towards external magnetic field. C. has susceptibility little more than zero. D. move from a region of strong magnetic field to weak magnetic field. Choose the most appropriate answer from the options given below:

Options:

A) A, B, C Only

B) A, C Only

C) A, B, C, D

D) B, D Only

MediumJEE Mains2025

Figure shows a current carrying square loop ABCD of edge length is ‘a’ lying in a plane. If the resistance of the ABC part is r and that of ADC part is 2r, then the magnitude of the resultant magnetic field at centre of the square loop is

Options:

A) \frac{2\mu_0 I}{3\pi a}

B) \frac{\sqrt{2}\mu_0 I}{3\pi a}

C) \frac{3\pi\mu_0 I}{\sqrt{2}a}

D) \frac{\mu_0 I}{2\pi a}

EasyJEE Mains2024

Match List I with List II: LIST I(Y vs X) LIST II(Shape of Graph) A. Y-magnetic susceptibilityX = magnetising field I. B. Y = magnetic fieldX = distance from centre of a current carrying wire for x < a (where a = radius of wire) II. C. Y = magnetic field$\mathrm{X}= distance from centre of a current carrying wire for x>\mathrm{a}(where \mathrm{a}=$ radius of wire) III. D. Y = magnetic field inside solenoidX = distance from centre IV. Choose the correct answer from the options given below :

Options:

A) (A)-(III), (B)-(IV), (C)- (I), (D)-(II)

B) (A)-(III), (B)-(I), (C)-(IV), (D)-(II)

C) (A)-(IV), (B)-(I), (C)-(III), (D)-(II)

D) (A)-(I), (B)-(III), (C)-(II), (D)-(IV)

EasyJEE Mains2025

A particle of charge q, mass m and kinetic energy E enters in magnetic field perpendicular to its velocity and undergoes a circular arc of radius (r). Which of the following curves represents the variation of r with E ?

Options:

EasyJEE Mains2024

The magnetic moment of a bar magnet is $0.5 \mathrm{~Am}^2. It is suspended in a uniform magnetic field of 8 \times 10^{-2} \mathrm{~T}$. The work done in rotating it from its most stable to most unstable position is:

Options:

A) 4 \times 10^{-2} \mathrm{~J}

B) 16 \times 10^{-2} \mathrm{~J}

C) 8 \times 10^{-2} \mathrm{~J}

D) Zero

MediumJEE Mains2025

Uniform magnetic fields of different strengths \left(B_1\right. and \left.B_2\right), both normal to the plane of the paper exist as shown in the figure. A charged particle of mass m and charge q, at the interface at an instant, moves into the region 2 with velocity v and returns to the interface. It continues to move into region 1 and finally reaches the interface. What is the displacement of the particle during this movement along the interface? (Consider the velocity of the particle to be normal to the magnetic field and \mathrm{B}_2>\mathrm{B}_1 )

Options:

A) \frac{m v}{q B_1}\left(1-\frac{B_1}{B_2}\right) \times 2

B) \frac{m v}{q B_1}\left(1-\frac{B_2}{B_1}\right) \times 2

C) \frac{m v}{q B_1}\left(1-\frac{B_2}{B_1}\right)

D) \frac{m v}{q B_1}\left(1-\frac{B_1}{B_2}\right)

EasyJEE Mains2023

Given below are two statements: Statement I : The diamagnetic property depends on temperature. Statement II : The induced magnetic dipole moment in a diamagnetic sample is always opposite to the magnetizing field. In the light of given statements, choose the correct answer from the options given below.

Options:

A) Statement I is incorrect but Statement II is true.

B) Statement I is correct but Statement II is false.

C) Both Statement I and Statement II are False.

D) Both Statement I and Statement II are true.

MediumJEE Mains2025

Given below are two statements: one is labelled as \mathbf{A s s e r t i o n} \mathbf{A} and the other is labelled as Reason \mathbf{R} Assertion A : If Oxygen ion \left(\mathrm{O}^{-2}\right) and Hydrogen ion \left(\mathrm{H}^{+}\right)enter normal to the magnetic field with equal momentum, then the path of \mathrm{O}^{-2} ion has a smaller curvature than that of \mathrm{H}^{+}. Reason R : A proton with same linear momentum as an electron will form a path of smaller radius of curvature on entering a uniform magnetic field perpendicularly. In the light of the above statements, choose the correct answer from the options given below

Options:

A) Both \mathbf{A} and \mathbf{R} are true but \mathbf{R} is NOT the correct explanation of \mathbf{A}

B) \mathbf{A} is false but \mathbf{R} is true

C) \mathbf{A} is true but \mathbf{R} is false

D) Both \mathbf{A} and \mathbf{R} are true and \mathbf{R} is the correct explanation of \mathbf{A}

MediumJEE Mains2023

The free space inside a current carrying toroid is filled with a material of susceptibility $2 \times 10^{-2}$. The percentage increase in the value of magnetic field inside the toroid will be

Options:

A) 0.1%

B) 1%

C) 2%

D) 0.2%

MediumJEE Mains2025

In a moving coil galvanometer, two moving coils \mathrm{M}_1 and \mathrm{M}_2 have the following particulars : $ \begin{aligned} & \mathrm{R}_1=5 \Omega, \mathrm{~N}_1=15, \mathrm{~A}_1=3.6 \times 10^{-3} \mathrm{~m}^2, \mathrm{~B}_1=0.25 \mathrm{~T} \\ & \mathrm{R}_2=7 \Omega, \mathrm{~N}_2=21, \mathrm{~A}_2=1.8 \times 10^{-3} \mathrm{~m}^2, \mathrm{~B}_2=0.50 \mathrm{~T} \end{aligned} Assuming that torsional constant of the springs are same for both coils, what will be the ratio of voltage sensitivity of M_1 and M_2$ ?

Options:

A) 1: 1

B) 1: 3

C) 1: 2

D) 1: 4

EasyJEE Mains2023

A bar magnet is released from rest along the axis of a very long vertical copper tube. After some time the magnet will

Options:

A) move down with almost constant speed

B) move down with an acceleration equal to $\mathrm{g}

C) move down with an acceleration greater than $\mathrm{g}

D) oscillate inside the tube

EasyJEE Mains2025

A solenoid having area A and length ' l ' is filled with a material having relative permeability 2. The magnetic energy stored in the solenoid is :

Options:

A) \frac{\mathrm{B}^2 \mathrm{~A} l}{4 \mu_0}

B) \frac{\mathrm{B}^2 \mathrm{~A} l}{2 \mu_0}

C) \frac{\mathrm{B}^2 \mathrm{~A} l}{\mu_0}

D) \mathrm{B}^2 \mathrm{Al}

EasyJEE Mains2023

Given below are two statements: Statement I : For diamagnetic substance, $-1 \leq \chi < 0, where \chi$ is the magnetic susceptibility. Statement II : Diamagnetic substances when placed in an external magnetic field, tend to move from stronger to weaker part of the field. In the light of the above statements, choose the correct answer from the options given below

Options:

A) Both Statement I and Statement II are true

B) Statement I is correct but Statement II is false

C) Both Statement I and Statement II are False

D) Statement I is incorrect but Statement II is true.

MediumJEE Mains2025

Let B_1 be the magnitude of magnetic field at center of a circular coil of radius R carrying current I. Let \mathrm{B}_2 be the magnitude of magnetic field at an axial distance ' x ' from the center. For x: \mathrm{R}=3: 4, \frac{\mathrm{~B}_2}{\mathrm{~B}_1} is :

Options:

A) 64: 125

B) 25: 16

C) 4: 5

D) 16: 25

EasyJEE Mains2023

Given below are two statements: one is labelled as Assertion $\mathbf{A} and the other is labelled as Reason \mathbf{R}$ Assertion A : Electromagnets are made of soft iron. Reason R : Soft iron has high permeability and low retentivity. In the light of above, statements, choose the most appropriate answer from the options given below.

Options:

A) Both A and R are correct and R is the correct explanation of A

B) A is not correct but R is correct

C) A is correct but R is not correct

D) Both A and R are correct but R is NOT the correct explanation of A

MediumJEE Mains2025

Consider a long straight wire of a circular cross-section (radius a) carrying a steady current I. The current is uniformly distributed across this cross-section. The distances from the centre of the wire’s cross-section at which the magnetic field [inside the wire, outside the wire] is half of the maximum possible magnetic field, any where due to the wire, will be :

Options:

A) [a/2, 3a]

B) [a/4, 3a/2]

C) [a/2, 2a]

D) [a/4, 2a]

EasyJEE Mains2023

A bar magnet with a magnetic moment $5.0 \mathrm{Am}^{2} is placed in parallel position relative to a magnetic field of 0.4 \mathrm{~T}$. The amount of required work done in turning the magnet from parallel to antiparallel position relative to the field direction is _____________.

Options:

A) zero

B) 1 J

C) 2 J

D) 4 J

MediumJEE Mains2025

An infinite wire has a circular bend of radius a, and carrying a current I as shown in the figure. The magnitude of magnetic field at the origin O of the arc is given by:

Options:

A) \frac{\mu_0}{2 \pi} \frac{\mathrm{I}}{\mathrm{a}}\left[\frac{\pi}{2}+2\right]

B) \frac{\mu_0}{4 \pi} \frac{\mathrm{I}}{\mathrm{a}}\left[\frac{3 \pi}{2}+1\right]

C) \frac{\mu_0}{4 \pi} \frac{\mathrm{I}}{\mathrm{a}}\left[\frac{\pi}{2}+1\right]

D) \frac{\mu_0}{4 \pi} \frac{\mathrm{I}}{\mathrm{a}}\left[\frac{3 \pi}{2}+2\right]

EasyJEE Mains2023

A solenoid of 1200 turns is wound uniformly in a single layer on a glass tube 2 m long and 0.2 m in diameter. The magnetic intensity at the center of the solenoid when a current of 2 A flows through it is :

Options:

A) \mathrm{1~A~m^{-1}}

B) \mathrm{2.4\times10^{-3}~A~m^{-1}}

C) \mathrm{1.2\times10^{3}~A~m^{-1}}

D) \mathrm{2.4\times10^{3}~A~m^{-1}}

HardJEE Mains2025

Consider a long thin conducting wire carrying a uniform current I. A particle having mass "M" and charge " q " is released at a distance " a " from the wire with a speed v_0 along the direction of current in the wire. The particle gets attracted to the wire due to magnetic force. The particle turns round when it is at distance x from the wire. The value of x is [ \mu_0 is vacuum permeability]

Options:

A) a\left[1-\frac{m v_o}{2 q \mu_0 \mathrm{I}}\right]

B) a e^{-\frac{4 \pi \mathrm{mv}_o}{q \mu_o \mathrm{I}}}

C) a\left[1-\frac{\mathrm{mv}}{\mathrm{q}} \mu_{\mathrm{o}} \mathrm{I}\right]

D) \frac{a}{2}

EasyJEE Mains2022

The vertical component of the earth's magnetic field is $6 \times 10^{-5} \mathrm{~T} at any place where the angle of dip is 37^{\circ}. The earth's resultant magnetic field at that place will be \left(\right.Given \left.\tan 37^{\circ}=\frac{3}{4}\right)

Options:

A) 8 \times 10^{-5} \mathrm{~T}

B) 6 \times 10^{-5} \mathrm{~T}

C) 5 \times 10^{-4} \mathrm{~T}

D) 1 \times 10^{-4} \mathrm{~T}

MediumJEE Mains2025

N equally spaced charges each of value q , are placed on a circle of radius R . The circle rotates about its axis with an angular velocity \omega as shown in the figure. A bigger Amperian loop B encloses the whole circle where as a smaller Amperian loop A encloses a small segment. The difference between enclosed currents, I_A-I_B, for the given Amperian loops is

Options:

A) \frac{\mathrm{N}^2}{2 \pi} \mathrm{q} \omega

B) \frac{\mathrm{N}}{2 \pi} \mathrm{q} \omega

C) \mathrm{\frac{2 \pi}{N} q \omega}

D) \frac{\mathrm{N}}{\pi} \mathrm{q} \omega

MediumJEE Mains2022

A compass needle of oscillation magnetometer oscillates 20 times per minute at a place $\mathrm{P} of \operatorname{dip} 30^{\circ}. The number of oscillations per minute become 10 at another place \mathrm{Q} of 60^{\circ} dip. The ratio of the total magnetic field at the two places \left(B_{Q}: B_{P}\right)$ is :

Options:

A) \sqrt{3}: 4

B) 4: \sqrt{3}

C) \sqrt{3}: 2

D) 2: \sqrt{3}

EasyJEE Mains2025

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : A electron in a certain region of uniform magnetic field is moving with constant velocity in a straight line path. Reason (R) : The magnetic field in that region is along the direction of velocity of the electron. In the light of the above statements, choose the correct answer from the options given below :

Options:

A) (A) is true but (R) is false

B) Both (A) and (R) are true and (R) is the correct explanation of (A)

C) Both (\mathbf{A}) and (\mathbf{R}) are true but (\mathbf{R}) is NOT the correct explanation of (A)

D) (A) is false but (R) is true

MediumJEE Mains2022

Two bar magnets oscillate in a horizontal plane in earth's magnetic field with time periods of $3 \mathrm{~s} and 4 \mathrm{~s} respectively. If their moments of inertia are in the ratio of 3: 2$, then the ratio of their magnetic moments will be:

Options:

A) 2 : 1

B) 8 : 3

C) 1 : 3

D) 27 : 16

EasyJEE Mains2025

A long straight wire of a circular cross-section with radius ' a ' carries a steady current I . The current I is uniformly distributed across this cross-section. The plot of magnitude of magnetic field B with distance r from the centre of the wire is given by

Options:

MediumJEE Mains2022

A magnet hung at $45^{\circ} with magnetic meridian makes an angle of 60^{\circ}$ with the horizontal. The actual value of the angle of dip is -

Options:

A) \tan ^{-1}\left(\sqrt{\frac{3}{2}}\right)

B) \tan ^{-1}(\sqrt{6})

C) \tan ^{-1}\left(\sqrt{\frac{2}{3}}\right)

D) \tan ^{-1}\left(\sqrt{\frac{1}{2}}\right)

MediumJEE Mains2025

An electron projected perpendicular to a uniform magnetic field B moves in a circle. If Bohr's quantization is applicable, then the radius of the electronic orbit in the first excited state is :

Options:

A) \sqrt{\frac{h}{\pi e B}}

B) \sqrt{\frac{4 h}{\pi e B}}

C) \sqrt{\frac{\mathrm{h}}{2 \pi e \mathrm{eB}}}

D) \sqrt{\frac{2 h}{\pi e B}}

EasyJEE Mains2022

An electron with energy 0.1 keV moves at right angle to the earth's magnetic field of 1 $\times 10-4 Wbm-2. The frequency of revolution of the electron will be : (Take mass of electron = 9.0 \times 10-$31 kg)

Options:

A) 1.6 \times 10^{5} \mathrm{~Hz}

B) 5.6 \times 10^{5} \mathrm{~Hz}

C) 2.8 \times 10^{6} \mathrm{~Hz}

D) 1.8 \times 10^{6} \mathrm{~Hz}

EasyJEE Mains2024

A proton and a deutron $(q=+\mathrm{e}, m=2.0 \mathrm{u}) having same kinetic energies enter a region of uniform magnetic field \vec{B}, moving perpendicular to \vec{B}. The ratio of the radius r_d of deutron path to the radius r_p$ of the proton path is:

Options:

A) 1: 2

B) 1: 1

C) \sqrt{2}: 1

D) 1: \sqrt{2}

EasyJEE Mains2022

At a certain place the angle of dip is 30$^\circ$ and the horizontal component of earth's magnetic field is 0.5 G. The earth's total magnetic field (in G), at that certain place, is :

Options:

A) {1 \over {\sqrt 3 }}

B) {1 \over 2}

C) \sqrt 3

D) 1

MediumJEE Mains2024

Given below are two statements : Statement (I) : When currents vary with time, Newton's third law is valid only if momentum carried by the electromagnetic field is taken into account Statement (II) : Ampere's circuital law does not depend on Biot-Savart's law. In the light of the above statements, choose the correct answer from the options given below :

Options:

A) Both Statement I and Statement II are false

B) Statement I is false but Statement II is true

C) Both Statement I and Statement II are true

D) Statement I is true but Statement II is false

EasyJEE Mains2022

The space inside a straight current carrying solenoid is filled with a magnetic material having magnetic susceptibility equal to 1.2 $\times 10-$5. What is fractional increase in the magnetic field inside solenoid with respect to air as medium inside the solenoid?

Options:

A) 1.2 $\times 10-$5

B) 1.2 $\times 10-$3

C) 1.8 $\times 10-$3

D) 2.4 $\times 10-$5

MediumJEE Mains2024

A long straight wire of radius a carries a steady current I. The current is uniformly distributed across its cross section. The ratio of the magnetic field at $\frac{a}{2} and 2 a$ from axis of the wire is :

Options:

A) 4: 1

B) 3: 4

C) 1: 1

D) 1: 4

EasyJEE Mains2022

The susceptibility of a paramagnetic material is 99. The permeability of the material in Wb/A-m, is : [Permeability of free space $\mu0 = 4\pi \times 10-$7 Wb/A-m]

Options:

A) 4$\pi \times 10-$7

B) 4$\pi \times 10-$4

C) 4$\pi \times 10-$5

D) 4$\pi \times 10-$6

EasyJEE Mains2024

An element $\Delta l=\Delta x\hat{i} is placed at the origin and carries a large current I=10 \mathrm{~A}. The magnetic field on the y-axis at a distance of 0.5 \mathrm{~m} from the elements \Delta x of 1 \mathrm{~cm}$ length is:

Options:

A) 10 \times 10^{-8} \mathrm{~T}

B) 8 \times 10^{-8} \mathrm{~T}

C) 4 \times 10^{-8} \mathrm{~T}

D) 12 \times 10^{-8} \mathrm{~T}

EasyJEE Mains2022

A bar magnet having a magnetic moment of 2.0 $\times 105 JT-1, is placed along the direction of uniform magnetic field of magnitude B = 14 \times 10-5 T. The work done in rotating the magnet slowly through 60^\circ$ from the direction of field is :

Options:

A) 14 J

B) 8.4 J

C) 4 J

D) 1.4 J

EasyJEE Mains2024

The electrostatic force $\left(\vec{F_1}\right) and magnetic force \left(\vec{F}_2\right) acting on a charge q moving with velocity v$ can be written :

Options:

A) \vec{F}_1=q \vec{B}, \vec{F}_2=q(\vec{B} \times \vec{v})

B) \vec{F}_1=q \vec{V} \cdot \vec{E}, \vec{F}_2=q(\vec{B} \cdot \vec{V})

C) \vec{F}_1=q \vec{E}, \vec{F}_2=q(\vec{V} \times \vec{B})

D) \vec{F}_1=q \vec{E}, \vec{F}_2=q(\vec{B} \times \vec{V})

EasyJEE Mains2022

Given below are two statements : Statement I : Susceptibilities of paramagnetic and ferromagnetic substances increase with decrease in temperature. Statement II : Diamagnetism is a result of orbital motions of electrons developing magnetic moments opposite to the applied magnetic field. Choose the correct answer from the options given below :

Options:

A) Both Statement I and Statement II are true.

B) Both Statement I and Statement II are false.

C) Statement I is true but Statement II is false.

D) Statement I is false but Statement II is true.

MediumJEE Mains2024

In a co-axial straight cable, the central conductor and the outer conductor carry equal currents in opposite directions. The magnetic field is zero :

Options:

A) inside the outer conductor

B) outside the cable

C) in between the two conductors

D) inside the inner conductor

EasyJEE Mains2022

The soft-iron is a suitable material for making an electromagnet. This is because soft-iron has

Options:

A) low coercivity and high retentivity.

B) low coercivity and low permeability.

C) high permeability and low retentivity.

D) high permeability and high retentivity.

EasyJEE Mains2024

An electron is projected with uniform velocity along the axis inside a current carrying long solenoid. Then :

Options:

A) the electron will experience a force at $45^{\circ}$ to the axis and execute a helical path.

B) the electron will be accelerated along the axis.

C) the electron path will be circular about the axis.

D) the electron will continue to move with uniform velocity along the axis of the solenoid.

MediumJEE Mains2021

Following plots show magnetization (M) vs magnetizing field (H) and magnetic susceptibility ($\chi $) vs temperature (T) graph :Which of the following combination will be represented by a diamagnetic material?

Options:

A) (a), (c)

B) (a), (d)

C) (b), (d)

D) (b), (c)

EasyJEE Mains2024

A uniform magnetic field of $2 \times 10^{-3} \mathrm{~T} acts along positive Y-direction. A rectangular loop of sides 20 \mathrm{~cm} and 10 \mathrm{~cm} with current of 5 \mathrm{~A} is in Y-Z plane. The current is in anticlockwise sense with reference to negative X$ axis. Magnitude and direction of the torque is:

Options:

A) 2 \times 10^{-4} \mathrm{~N}- \mathrm{m} along negative Z$-direction

B) 2 \times 10^{-4} \mathrm{~N} - \mathrm{m} along positive X$-direction

C) 2 \times 10^{-4} \mathrm{~N} - \mathrm{m} along positive Y$-direction

D) 2 \times 10^{-4} \mathrm{~N} - \mathrm{m} along positive Z$-direction

MediumJEE Mains2021

Choose the correct option

Options:

A) True dip is always equal to apparent dip.

B) True dip is not mathematically related to apparent dip.

C) True dip is less than the apparent dip.

D) True dip is always greater than the apparent dip.

MediumJEE Mains2024

A rigid wire consists of a semicircular portion of radius $R and two straight sections. The wire is partially immerged in a perpendicular magnetic field B=B_0 \hat{k} as shown in figure. The magnetic force on the wire if it has a current i$ is:

Options:

A) i B R \hat{j}

B) -2 i B R \hat{j}

C) 2 i B R \hat{j}

D) -i B R \hat{j}

EasyJEE Mains2021

Statement I : The ferromagnetic property depends on temperature. At high temperature, ferromagnet becomes paramagnet.Statement II : At high temperature, the domain wall area of a ferromagnetic substance increases.In the light of the above statements, choose the most appropriate answer from the options given below :

Options:

A) Statement I is false but Statement II is true

B) Statement I is true but Statement II is false

C) Both Statement I and Statement II are false

D) Both Statement I and Statement II are true

EasyJEE Mains2024

Two insulated circular loop A and B of radius '$a' carrying a current of '\mathrm{I}$' in the anti clockwise direction as shown in the figure. The magnitude of the magnetic induction at the centre will be :

Options:

A) \frac{\sqrt{2} \mu_0 I}{a}

B) \frac{\mu_0 I}{\sqrt{2} a}

C) \frac{\mu_0 \mathrm{I}}{2 \mathrm{a}}

D) \frac{2 \mu_0 I}{a}

MediumJEE Mains2021

At an angle of 30$^\circ to the magnetic meridian, the apparent dip is 45^\circ$. Find the true dip :

Options:

A) {\tan ^{ - 1}}\sqrt 3

B) {\tan ^{ - 1}}{1 \over {\sqrt 3 }}

C) {\tan ^{ - 1}}{2 \over {\sqrt 3 }}

D) {\tan ^{ - 1}}{{\sqrt 3 } \over 2}

EasyJEE Mains2024

Two particles $X and Y having equal charges are being accelerated through the same potential difference. Thereafter they enter normally in a region of uniform magnetic field and describes circular paths of radii R_1 and R_2 respectively. The mass ratio of X and Y$ is :

Options:

A) \left(\frac{R_1}{R_2}\right)

B) \left(\frac{R_2}{R_1}\right)

C) \left(\frac{R_2}{R_1}\right)^2

D) \left(\frac{R_1}{R_2}\right)^2

EasyJEE Mains2021

The magnetic susceptibility of a material of a rod is 499. Permeability in vacuum is 4$\pi \times 10-$7 H/m. Absolute permeability of the material of the rod is :

Options:

A) 4$\pi \times 10-$4 H/m

B) 2$\pi \times 10-$4 H/m

C) 3$\pi \times 10-$4 H/m

D) \pi \times 10-$4 H/m

MediumJEE Mains2024

A proton moving with a constant velocity passes through a region of space without any change in its velocity. If $\overrightarrow{\mathrm{E}} and \overrightarrow{\mathrm{B}} represent the electric and magnetic fields respectively, then the region of space may have : (A) \mathrm{E}=0, \mathrm{~B}=0 (B) \mathrm{E}=0, \mathrm{~B} \neq 0 (C) \mathrm{E} \neq 0, \mathrm{~B}=0 (D) \mathrm{E} \neq 0, \mathrm{~B} \neq 0$ Choose the most appropriate answer from the options given below :

Options:

A) (A), (B) and (C) only

B) (A), (C) and (D) only

C) (A), (B) and (D) only

D) (B), (C) and (D) only

MediumJEE Mains2021

Which of the following statements are correct?(A) Electric monopoles do not exist whereas magnetic monopoles exist.(B) Magnetic field lines due to a solenoid at its ends and outside cannot be completely straight and confined.(C) Magnetic field lines are completely confined within a toroid.(D) Magnetic field lines inside a bar magnet are not parallel.(E) $\chi = -$1 is the condition for a perfect diamagnetic material, where x is its magnetic susceptibility.Choose the correct answer from the options given below :

Options:

A) (A) and (B) only

B) (B) and (C) only

C) (C) and (E) only

D) (B) and (D) only

EasyJEE Mains2023

An electron is moving along the positive $\mathrm{x}-axis. If the uniform magnetic field is applied parallel to the negative z-axis, then A. The electron will experience magnetic force along positive y-axis B. The electron will experience magnetic force along negative y-axis C. The electron will not experience any force in magnetic field D. The electron will continue to move along the positive \mathrm{x}$-axis E. The electron will move along circular path in magnetic field Choose the correct answer from the options given below:

Options:

A) A and E only

B) B and D only

C) B and E only

D) C and D only

MediumJEE Mains2021

A bar magnet of length 14 cm is placed in the magnetic meridian with its north pole pointing towards the geographic north pole. A neutral point is obtained at a distance of 18 cm from the center of the magnet. If BH = 0.4 G, the magnetic moment of the magnet is : (1G = 10$-$4 T)

Options:

A) 2.880 $\times 102 J T-$1

B) 2.880 J T$-$1

C) 2.880 $\times 103 J T-$1

D) 28.80 J T$-$1

MediumJEE Mains2023

The source of time varying magnetic field may be (A) a permanent magnet (B) an electric field changing linearly with time (C) direct current (D) a decelerating charge particle (E) an antenna fed with a digital signal Choose the correct answer from the options given below:

Options:

A) (D) only

B) (A) only

C) (B) and (D) only

D) (C) and (E) only

EasyJEE Mains2021

In a ferromagnetic material, below the curie temperature, a domain is defined as :

Options:

A) a macroscopic region with zero magnetization.

B) a macroscopic region with saturation magnetization.

C) a macroscopic region with randomly oriented magnetic dipoles.

D) a macroscopic region with consecutive magnetic dipoles oriented in opposite direction.

EasyJEE Mains2023

An electron is allowed to move with constant velocity along the axis of current carrying straight solenoid. A. The electron will experience magnetic force along the axis of the solenoid. B. The electron will not experience magnetic force. C. The electron will continue to move along the axis of the solenoid. D. The electron will be accelerated along the axis of the solenoid. E. The electron will follow parabolic path-inside the solenoid. Choose the correct answer from the options given below:

Options:

A) B, C and D only

B) B and C only

C) A and D only

D) B and E only

EasyJEE Mains2021

A soft ferromagnetic material is placed in an external magnetic field. The magnetic domains :

Options:

A) may increase or decrease in size and change its orientation.

B) increase in size but no change in orientation.

C) decrease in size and changes orientation.

D) have no relation with external magnetic field.

EasyJEE Mains2023

A charge particle moving in magnetic field B, has the components of velocity along B as well as perpendicular to B. The path of the charge particle will be

Options:

A) helical path with the axis along magnetic field $\mathrm{B}

B) straight along the direction of magnetic field $\mathrm{B}

C) circular path

D) helical path with the axis perpendicular to the direction of magnetic field B

MediumJEE Mains2020

A paramagnetic sample shows a net magnetisation of 6 A/m when it is placed in an external magnetic field of 0.4 T at a temperature of 4 K. When the sample is placed in an external magnetic field of 0.3 T at a temperature of 24 K, then the magnetisation will be:

Options:

A) 4 A/m

B) 1 A/m

C) 0.75 A/m

D) 2.25 A/m

EasyJEE Mains2023

A long straight wire of circular cross-section (radius a) is carrying steady current I. The current I is uniformly distributed across this cross-section. The magnetic field is

Options:

A) uniform in the region $r < a and inversely proportional to distance r from the axis, in the region r > a

B) zero in the region $r < a and inversely proportional to r in the region r > a

C) directly proportional to $r in the region r < a and inversely proportional to r in the region r > a

D) inversely proportional to $r in the region r < a and uniform throughout in the region r > a

MediumJEE Mains2020

A small bar magnet placed with its axis at 30o with an external field of 0.06 T experiences a torque of 0.018 Nm. The minimum work required to rotate it from its stable to unstable equilibrium position is :

Options:

A) 6.4 $ \times $ 10-2 J

B) 9.2 $ \times $ 10-3 J

C) 7.2 $ \times $ 10-2 J

D) 11.7 $ \times $ 10-3 J

MediumJEE Mains2023

As shown in the figure, a long straight conductor with semicircular arc of radius $\frac{\pi}{10}m is carrying current \mathrm{I=3A}. The magnitude of the magnetic field, at the center O of the arc is : (The permeability of the vacuum =4\pi\times10^{-7}~\mathrm{NA}^{-2}$)

Options:

A) 4\mu\mathrm{T}

B) 3\mu\mathrm{T}

C) 6\mu\mathrm{T}

D) 1\mu\mathrm{T}

MediumJEE Mains2020

A perfectly diamagnetic sphere has a small spherical cavity at its centre, which is filled with a paramagnetic substance. The whole system is placed in a uniform magnetic field $\overrightarrow B $ . Then the field inside the paramagnetic substance is :

Options:

A) \overrightarrow B

B) zero

C) much large than $\left| {\overrightarrow B } \right| and parallel to \overrightarrow B

D) much large than $\left| {\overrightarrow B } \right| but opposite to \overrightarrow B

MediumJEE Mains2023

Find the magnetic field at the point $\mathrm{P}$ in figure. The curved portion is a semicircle connected to two long straight wires.

Options:

A) \frac{\mu_{0} i}{2 r}\left(\frac{1}{2}+\frac{1}{2 \pi}\right)

B) \frac{\mu_{\mathrm{o}} i}{2 r}\left(1+\frac{2}{\pi}\right)

C) \frac{\mu_{0} \dot{i}}{2 r}\left(\frac{1}{2}+\frac{1}{\pi}\right)

D) \frac{\mu_{0} i}{2 r}\left(1+\frac{1}{\pi}\right)

MediumJEE Mains2020

Magnetic materials used for making permanent magnets (P) and magnets in a transformer (T) have different properties of the following, which property best matches for the type of magnet required?

Options:

A) T : Large retentivity, small coercivity

B) P : Large retentivity, large coercivity

C) P : Small retentivity, large coercivity

D) T : Large retentivity, large coercivity

MediumJEE Mains2023

A long conducting wire having a current I flowing through it, is bent into a circular coil of \mathrm{N} turns. Then it is bent into a circular coil of \mathrm{n} turns. The magnetic field is calculated at the centre of coils in both the cases. The ratio of the magnetic field in first case to that of second case is :

Options:

A) N^{2}: n^{2}

B) \mathrm{N}: \mathrm{n}

C) \mathrm{n}: \mathrm{N}

D) n^{2}: N^{2}

MediumJEE Mains2020

The figure gives experimentally measured B vs H variation in a ferromagnetic material. The retentivity, coercivity and saturation, respectively, of the material are :

Options:

A) 1.0 T, 50A/m and 1.5 T

B) 1.5 T, 50 A/m and 1.0 T

C) 1.5 T, 50 A/m and 2.0 T

D) 150 A/m, 1.0 T and 1.5 T

MediumJEE Mains2023

A rod with circular cross-section area $2 \mathrm{~cm}^{2} and length 40 \mathrm{~cm} is wound uniformly with 400 turns of an insulated wire. If a current of 0.4 \mathrm{~A} flows in the wire windings, the total magnetic flux produced inside windings is 4 \pi \times 10^{-6} \mathrm{~Wb}. The relative permeability of the rod is (Given : Permeability of vacuum \mu_{0}=4 \pi \times 10^{-7} \mathrm{NA}^{-2}$)

Options:

A) \frac{5}{16}

B) 125

C) \frac{32}{5}

D) 12.5

MediumJEE Mains2019

A magnetic compass needle oscillates 30 times per minute at a place where the dip is 45o, and 40 times per minute where the dip is 30o. If B1 and B2 are respectively the total magnetic field due to the earth at the two places, then the ratio ${{{B_1}} \over {{B_2}}}$ is best given by :

Options:

A) 1.8

B) 2.2

C) 0.7

D) 3.6

MediumJEE Mains2023

As shown in the figure, a current of 2 \mathrm{~A} flowing in an equilateral triangle of side 4 \sqrt{3} \mathrm{~cm}. The magnetic field at the centroid \mathrm{O} of the triangle is (Neglect the effect of earth's magnetic field)

Options:

A) 4 \sqrt{3} \times 10^{-4} \mathrm{~T}

B) 4 \sqrt{3} \times 10^{-5} \mathrm{~T}

C) 3 \sqrt{3} \times 10^{-5} \mathrm{~T}

D) \sqrt{3} \times 10^{-4} \mathrm{~T}

MediumJEE Mains2019

Two magnetic dipoles X and Y are placed at a separation d, with their axes perpendicular to each other. The dipole moment of Y is twice that of X. A particle of charge q is passing, through their midpoint P, at angle q = 45° with the horizontal line, as shown in figure. What would be the magnitude of force on the particle at that instant ? (d is much larger than the dimensions of the dipole)

Options:

A) \left( {{{{\mu _0}} \over {4\pi }}} \right){2M \over {{{\left( {d/2} \right)}^3}}} \times qv

B) \left( {{{{\mu _0}} \over {4\pi }}} \right){M \over {{{\left( {d/2} \right)}^3}}} \times qv

C) \sqrt 2 \left( {{{{\mu _0}} \over {4\pi }}} \right){M \over {{{\left( {d/2} \right)}^3}}} \times qv

D) 0

EasyJEE Mains2023

A current carrying rectangular loop PQRS is made of uniform wire. The length P R=Q S=5 \mathrm{~cm} and P Q=R S=100 \mathrm{~cm}. If ammeter current reading changes from I to 2 I, the ratio of magnetic forces per unit length on the wire P Q due to wire R S in the two cases respectively \left(f_{P Q}^I: f_{P Q}^{2 t}\right) is:

Options:

A) 1 : 4

B) 1 : 3

C) 1 : 2

D) 1 : 5

MediumJEE Mains2019

A paramagnetic material has 1028 atoms/m3. Its magnetic susceptibility at temperature 350 K is 2.8 $ \times $ 10–4. Its susceptibility at 300 K is :

Options:

A) 3.726 $ \times $ 10–4

B) 2.672 $ \times $ 10–4

C) 3.672 $ \times $ 10–4

D) 3.267 $ \times 10-$4

MediumJEE Mains2023

A massless square loop, of wire of resistance $10 \Omega, supporting a mass of 1 \mathrm{~g}, hangs vertically with one of its sides in a uniform magnetic field of 10^{3} \mathrm{G}, directed outwards in the shaded region. A dc voltage \mathrm{V} is applied to the loop. For what value of \mathrm{V}, the magnetic force will exactly balance the weight of the supporting mass of 1 \mathrm{~g} ? (If sides of the loop =10 \mathrm{~cm}, \mathrm{~g}=10 \mathrm{~ms}^{-2}$)

Options:

A) 1 V

B) \frac{1}{10}$V

C) 10 V

D) 100 V

MediumJEE Mains2019

A paramagnetic substance in the form of a cube with sides 1 cm has a magnetic dipole moment of 20 $ \times 10–6 J/ T when a magnetic intensity of 60 \times $ 103 A/m is applied. Its magnetic susceptibility is

Options:

A) 3.3 $ \times $ 10–4

B) 2.3 $ \times $ 10–2

C) 4.3 $ \times $ 10–2

D) 3.3 $ \times $ 10–2

EasyJEE Mains2023

The magnetic moments associated with two closely wound circular coils $\mathrm{A} and \mathrm{B} of radius \mathrm{r}_{\mathrm{A}}=10 \mathrm{cm} and \mathrm{r}_{\mathrm{B}}=20 \mathrm{~cm} respectively are equal if : (Where \mathrm{N}_{\mathrm{A}}, \mathrm{I}_{\mathrm{A}} and \mathrm{N}_{\mathrm{B}}, \mathrm{I}_{\mathrm{B}} are number of turn and current of \mathrm{A} and \mathrm{B}$ respectively)

Options:

A) 4 \mathrm{~N}_{\mathrm{A}} \mathrm{I}_{\mathrm{A}}=\mathrm{N}_{\mathrm{B}} \mathrm{I}_{\mathrm{B}}

B) 2 \mathrm{~N}_{\mathrm{A}} \mathrm{I}_{\mathrm{A}}=\mathrm{N}_{\mathrm{B}} \mathrm{I}_{\mathrm{B}}

C) \mathrm{N}_{\mathrm{A}}=2 \mathrm{~N}_{\mathrm{B}}

D) \mathrm{N}_{\mathrm{A}} \mathrm{I}_{\mathrm{A}}=4 \mathrm{~N}_{\mathrm{B}} \mathrm{I}_{\mathrm{B}}

MediumJEE Mains2019

At some location on earth, the horizontal component of earth’s magnetic field is 18 × 10–6 T. At this location, magnetic needle of length 0.12 m and pole strength 1.8 Am is suspended from its mid-point using a thread, it makes 45o angle with horizontal in equilibrium. To keep this needle horizontal, the vertical force that should be applied at one of its ends is -

Options:

A) 3.6 $ \times 10-$5 N

B) 1.8 $ \times 10-$5 N

C) 1.3 $ \times 10-$5 N

D) 6.5 $ \times 10-$5 N

MediumJEE Mains2023

The electric current in a circular coil of four turns produces a magnetic induction 32 T at its centre. The coil is unwound and is rewound into a circular coil of single turn, the magnetic induction at the centre of the coil by the same current will be :

Options:

A) 2 T

B) 4 T

C) 8 T

D) 16 T

MediumJEE Mains2019

A magnet of total magnetic moment 10-2 ${\widehat i} A-m2 is placed in a time varying magnetic field, B{\widehat i} (cos \omega t) where B = 1 Tesla and \omega $ = 0.125 rad/s. The work done for reversing the direction of the magnetic moment at t = 1 second, is -

Options:

A) 0.014 J

B) 0.028 J

C) 0.01 J

D) 0.007 J

MediumJEE Mains2023

The magnitude of magnetic induction at mid point $\mathrm{O}$ due to current arrangement as shown in Fig will be

Options:

A) \frac{\mu_{0} I}{\pi a}

B) \frac{\mu_{0} I}{4 \pi a}

C) \frac{\mu_{0} I}{2 \pi a}

D) 0

MediumJEE Mains2019

A bar magnet is demagnetized by inserting it inside a solenoid of length 0.2 m, 100 turns, and carrying a current of 5.2 A. The corecivity of the bar magnet is :

Options:

A) 285 A/m

B) 2600 A/m

C) 520 A/m

D) 1200 A/m

HardJEE Mains2023

A single current carrying loop of wire carrying current I flowing in anticlockwise direction seen from +ve $\mathrm{z} direction and lying in x y plane is shown in figure. The plot of \hat{j} component of magnetic field (By) at a distance 'a' (less than radius of the coil) and on y z plane vs z$ coordinate looks like

Options:

MediumJEE Mains2018

The $B-H curve for a ferromagnet is shown in the figure. The ferromagnet is placed inside a long solended with 1000$ turns/cm. The current that should be passed in the solended to demagnetise the ferromagnet completely is :

Options:

A) 1 mA

B) 2 mA

C) 20\,\mu A

D) 40\,\mu A

100

EasyJEE Mains2023

For a moving coil galvanometer, the deflection in the coil is 0.05 rad when a current of 10 mA is passes through it. If the torsional constant of suspension wire is $4.0\times10^{-5}\mathrm{N~m~rad^{-1}}, the magnetic field is 0.01T and the number of turns in the coil is 200, the area of each turn (in cm^2$) is :

Options:

A) 1.5

B) 2.0

C) 0.5

D) 1.0

101

MediumJEE Mains2017

A magnetic needle of magnetic moment 6.7 $\times 10-2 A m2 and moment of inertia 7.5 \times$ 10-6 kg m2 is performing simple harmonic oscillations in a magnetic field of 0.01 T. Time taken for 10 complete oscillations is:

Options:

A) 8.76 s

B) 6.65 s

C) 8.89 s

D) 6.98 s

102

HardJEE Mains2023

Match List I with List II List I(Current configuration) List II(Magnitude of Magnetic Field at point O) A. I. ${B_0} = {{{\mu _0}I} \over {4\pi r}}[\pi + 2] B. II. {B_0} = {{{\mu _0}} \over {4 }}{I \over r} C. III. {B_0} = {{{\mu _0}I} \over {2\pi r}}[\pi - 1] D. IV. {B_0} = {{{\mu _0}I} \over {4\pi r}}[\pi + 1]$ Choose the correct answer from the options given below :

Options:

A) A-III, B-IV, C-I, D-II

B) A-II, B-I, C-IV, D-III

C) A-III, B-I, C-IV, D-II

D) A-I, B-III, C-IV, D-II

103

MediumJEE Mains2016

A fighter plane of length 20 m, wing span (distance from tip of one wing to the tip of the other wing) of 15 m and height 5 m is flying towards east over Delhi. Its speed is 240 ms−1. The earth’s magnetic field over Delhi is 5 $ \times 10−5 T with the declination angle ~ 0o and dip of \theta such that sin \theta $ = 2/3 . If the voltage developed is VB between the lower and upper side of the plane and VW between the tips of the wings then VB and VW are close to :

Options:

A) VB = 45 mV; VW = 120 mV with right side of pilot at higher voltage

B) VB = 45 mV; VW = 120 mV with left side of pilot at higher voltage

C) VB = 40 mV; VW = 135 mV with right side of pilot at high voltage

D) VB = 40 mV; VW = 135 mV with left side of pilot at higher voltage

104

EasyJEE Mains2023

A long solenoid is formed by winding 70 turns cm$^{-1}. If 2.0 A current flows, then the magnetic field produced inside the solenoid is ____________ (\mu_0=4\pi\times10^{-7} TmA^{-1}$)

Options:

A) 88\times10^{-4}$ T

B) 1232\times10^{-4}$ T

C) 176\times10^{-4}$ T

D) 352\times10^{-4}$ T

105

MediumJEE Mains2016

Hysteresis loops for two magnetic materials $A and B$ are given below : These materials are used to make magnets for electric generators, transformer core and electromagnet core. Then it is proper to use :

Options:

A) A for transformers and B$ for electric generators.

B) B$ for electromagnets and transformers.

C) A$ for electric generators and transformers.

D) A for electromagnets and B$ for electric generators.

106

EasyJEE Mains2023

Two long straight wires P and Q carrying equal current 10A each were kept parallel to each other at 5 cm distance. Magnitude of magnetic force experienced by 10 cm length of wire P is F$_1. If distance between wires is halved and currents on them are doubled, force F_2$ on 10 cm length of wire P will be:

Options:

A) \frac{F_1}{8}

B) 10 F$_1

C) \frac{F_1}{10}

D) 8 F$_1

107

MediumJEE Mains2014

The coercivity of a small magnet where the ferromagnet gets demagnetized is $3 \times {10^3}\,A{m^{ - 1}}. The current required to be passed in a solenoid of length 10 cm and number of turns 100,$ so that the magnet gets demagnetized when inside the solenoid, is :

Options:

A) 30 mA

B) 60 mA

C) 3 A

D) 6A

108

EasyJEE Mains2023

A circular loop of radius $r$ is carrying current I A. The ratio of magnetic field at the center of circular loop and at a distance r from the center of the loop on its axis is :

Options:

A) 3$\sqrt2$ : 2

B) 1 : 3$\sqrt2

C) 2$\sqrt2$ : 1

D) 1 : $\sqrt2

109

MediumJEE Mains2013

Two short bar magnets of length $1 cm each have magnetic moments 1.20 A{m^2} and 1.00 A{m^2} respectively. They are placed on a horizontal table parallel to each other with their N poles pointing towards the South. They have a common magnetic equator and are separated by a distance of 20.0 cm. The value of the resultant horizontal magnetic induction at the mid-point O of the line joining their centres is close to \left( \, \right. Horizontal component of earth's magnetic induction is 3.6 \times 10.5Wb/{m^2})

Options:

A) 3.6 \times 10.5\,\,Wb/{m^2}

B) 2.56 \times 10.4\,\,Wb/{m^2}

C) 3.50 \times 10.4\,\,Wb/{m^2}

D) 5.80 \times 10.4\,Wb/{m^2}

110

EasyJEE Mains2022

A wire X of length $50 \mathrm{~cm} carrying a current of 2 \mathrm{~A} is placed parallel to a long wire \mathrm{Y} of length 5 \mathrm{~m}. The wire \mathrm{Y} carries a current of 3 \mathrm{~A}. The distance between two wires is 5 \mathrm{~cm} and currents flow in the same direction. The force acting on the wire \mathrm{Y}$ is

Options:

A) 1.2 \times 10^{-5} \mathrm{~N} directed towards wire \mathrm{X}$.

B) 1.2 \times 10^{-4} \mathrm{~N} directed away from wire \mathrm{X}$.

C) 1.2 \times 10^{-4} \mathrm{~N} directed towards wire \mathrm{X}$.

D) 2.4 \times 10^{-5} \mathrm{~N} directed towards wire \mathrm{X}$.

111

MediumJEE Mains2008

Relative permittivity and permeability of a material ${\varepsilon _r} and {\mu _r},$ respectively. Which of the following values of these quantities are allowed for a diamagnetic material?

Options:

A) {\varepsilon _r} = 0.5,\,\,{\mu _r} = 1.5

B) {\varepsilon _r} = 1.5,\,\,{\mu _r} = 0.5

C) {\varepsilon _r} = 0.5,\,\,{\mu _r} = 0.5

D) {\varepsilon _r} = 1.5,\,\,{\mu _r} = 1.5

112

EasyJEE Mains2022

A triangular shaped wire carrying $10 \mathrm{~A} current is placed in a uniform magnetic field of 0.5 \mathrm{~T}, as shown in figure. The magnetic force on segment \mathrm{CD} is (Given \mathrm{BC}=\mathrm{CD}=\mathrm{BD}=5 \mathrm{~cm}$.)

Options:

A) 0.126 N

B) 0.312 N

C) 0.216 N

D) 0.245 N

113

MediumJEE Mains2006

Needles ${N_1}, {N_2} and {N_3}$ are made of ferromagnetic, a paramagnetic and a diamagnetic substance respectively. A magnet when brought close to them will

Options:

A) attract ${N_1} and {N_2} strongly but repel {N_3}

B) attract ${N_1} strongly, {N_2} weakly and repel {N_3}$ weakly

C) attract ${N_1} strongly, but repel {N_2} and {N_3}$ weakly

D) attract all three of them

114

EasyJEE Mains2022

The magnetic field at the center of current carrying circular loop is $B_{1}. The magnetic field at a distance of \sqrt{3} times radius of the given circular loop from the center on its axis is B_{2}. The value of B_{1} / B_{2}$ will be

Options:

A) 9 : 4

B) 12 : $\sqrt5

C) 8 : 1

D) 5 : $\sqrt3

115

MediumJEE Mains2005

A magnetic needle is kept in a non-uniform magnetic field. It experiences :

Options:

A) neither a force nor a torque

B) a torque but not a force

C) a force but not a torque

D) a force and a torque

116

EasyJEE Mains2022

The current sensitivity of a galvanometer can be increased by : (A) decreasing the number of turns (B) increasing the magnetic field (C) decreasing the area of the coil (D) decreasing the torsional constant of the spring Choose the most appropriate answer from the options given below :

Options:

A) (B) and (C) only

B) (C) and (D) only

C) (A) and (C) only

D) (B) and (D) only

117

MediumJEE Mains2004

The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a vibration magnetometer is $2s.$ The magnet is cut along its length into three equal parts and these parts are then placed on each other with their like poles together. The time period of this combination will be

Options:

A) 2\sqrt 3 \,s

B) {2 \over 3}\,\,s

C) 2\,s

D) {2 \over {\sqrt 3 }}\,s

118

MediumJEE Mains2022

As shown in the figure, a metallic rod of linear density $0.45 \mathrm{~kg} \mathrm{~m}^{-1} is lying horizontally on a smooth inclined plane which makes an angle of 45^{\circ} with the horizontal. The minimum current flowing in the rod required to keep it stationary, when 0.15 \mathrm{~T} magnetic field is acting on it in the vertical upward direction, will be : {Use g=10 \mathrm{~m} / \mathrm{s}^{2}$}

Options:

A) 30 A

B) 15 A

C) 10 A

D) 3 A

119

MediumJEE Mains2004

The materials suitable for making electromagnets should have

Options:

A) high retentivity and low coercivity

B) low retentivity and low coercivity

C) high retentivity and high coercivity

D) low retentivity and high coercivity

120

EasyJEE Mains2022

A cyclotron is used to accelerate protons. If the operating magnetic field is $1.0 \mathrm{~T} and the radius of the cyclotron 'dees' is 60 \mathrm{~cm}, the kinetic energy of the accelerated protons in MeV will be : [\mathrm{use} \,\,\mathrm{m}_{\mathrm{p}}=1.6 \times 10^{-27} \mathrm{~kg}, \mathrm{e}=1.6 \times 10^{-19} \,\mathrm{C}$ ]

Options:

A) 12

B) 18

C) 16

D) 32

121

MediumJEE Mains2004

Curie temperature is the temperature above which

Options:

A) a ferromagnetic material becomes paramagnetic

B) a paramagnetic material becomes diamagnetic

C) a ferromagnetic material becomes diamagnetic

D) a paramagnetic material becomes ferromagnetic

122

EasyJEE Mains2022

Two concentric circular loops of radii $r_{1}=30 \mathrm{~cm} and r_{2}=50 \mathrm{~cm} are placed in \mathrm{X}-\mathrm{Y} plane as shown in the figure. A current I=7 \mathrm{~A}$ is flowing through them in the direction as shown in figure. The net magnetic moment of this system of two circular loops is approximately :

Options:

A) \frac{7}{2} \hat{k} \,\mathrm{Am}^{2}

B) -\frac{7}{2} \hat{k} \,\mathrm{Am}^{2}

C) {7}\, \hat{k} \,\mathrm{Am}^{2}

D) {-7}\, \hat{k} \,\mathrm{Am}^{2}

123

MediumJEE Mains2003

A magnetic needle lying parallel to a magnetic field requires $W units of work to turn it through {60^ \circ }.$ The torque needed to maintain the needle in this position will be :

Options:

A) \sqrt 3 \,W

B) W

C) {{\sqrt 3 } \over 2}W

D) 2W

124

EasyJEE Mains2022

A charge particle is moving in a uniform magnetic field $(2 \hat{i}+3 \hat{j}) \,\mathrm{T}. If it has an acceleration of (\alpha \hat{i}-4 \hat{j})\, \mathrm{m} / \mathrm{s}^{2}, then the value of \alpha$ will be :

Options:

A) 3

B) 6

C) 12

D) 2

125

MediumJEE Mains2003

A thin rectangular magnet suspended freely has a period of oscillation equal to $T. Now it is broken into two equal halves (each having half of the original length) and one piece is made to oscillate freely in the same field. If its period of oscillation is T', the ratio {{T'} \over T}$ is

Options:

A) {1 \over {2\sqrt 2 }}

B) {1 \over 2}

C) 2

D) {1 \over 4}

126

EasyJEE Mains2022

\mathrm{B}_{X} and \mathrm{B}_{\mathrm{Y}} are the magnetic fields at the centre of two coils \mathrm{X} and \mathrm{Y} respectively each carrying equal current. If coil X has 200 turns and 20 \mathrm{~cm} radius and coil Y has 400 turns and 20 \mathrm{~cm} radius, the ratio of B_{X} and B_{Y}$ is :

Options:

A) 1 : 1

B) 1 : 2

C) 2 : 1

D) 4 : 1

127

MediumJEE Mains2003

The magnetic lines of force inside a bar magnet

Options:

A) are from north-pole to south-pole of the magnet

B) do not exist

C) depend upon the area of cross-section of the bar magnet

D) are from south-pole to north-pole of the Magnet

128

EasyJEE Mains2022

Two charged particles, having same kinetic energy, are allowed to pass through a uniform magnetic field perpendicular to the direction of motion. If the ratio of radii of their circular paths is $6: 5 and their respective masses ratio is 9: 4$. Then, the ratio of their charges will be :

Options:

A) 8 : 5

B) 5 : 4

C) 5 : 3

D) 8 : 7

129

MediumJEE Mains2026

A short bar magnet placed with its axis at 30^{\circ} with an external field of 800 Gauss, experiences a torque of 0.016 \mathrm{~N} . \mathrm{m}. The work done in moving it from most stable to most unstable position is \alpha \times 10^{-3} \mathrm{~J}. The value of \alpha is \_\_\_\_ .

Options:

130

MediumJEE Mains2022

A coil of n number of turns wound tightly in the form of a spiral with inner and outer radii r1 and r2 respectively. When a current of strength I is passed through the coil, the magnetic field at its centre will be :

Options:

A) {{{\mu _0}nI} \over {2({r_2} - {r_1})}}

B) {{{\mu _0}nI} \over {{r_2}}}

C) {{{\mu _0}nI} \over {{r_2} - {r_1}}}{\log _e}{{{r_1}} \over {{r_2}}}

D) {{{\mu _0}nI} \over {2({r_2} - {r_1})}}{\log _e}{{{r_2}} \over {{r_1}}}

131

EasyJEE Mains2024

The coercivity of a magnet is $5 \times 10^3 \mathrm{~A} / \mathrm{m}. The amount of current required to be passed in a solenoid of length 30 \mathrm{~cm}$ and the number of turns 150, so that the magnet gets demagnetised when inside the solenoid is ________ A.

Options:

132

MediumJEE Mains2022

A cyclotron is working at a frequency of 10 MHz. If the radius of its dees is 60 cm. The maximum kinetic energy of accelerated proton will be : (Take : e = 1.6 $\times 10-19 C, mp = 1.67 \times 10-$27 kg)

Options:

A) 7.4 MeV

B) 14.86 MeV

C) 7.4 GeV

D) 704 GeV

133

EasyJEE Mains2024

The horizontal component of earth's magnetic field at a place is $3.5 \times 10^{-5} \mathrm{~T}. A very long straight conductor carrying current of \sqrt{2} \mathrm{~A} in the direction from South east to North West is placed. The force per unit length experienced by the conductor is __________ \times 10^{-6} \mathrm{~N} / \mathrm{m}$.

Options:

134

MediumJEE Mains2022

Two long current carrying conductors are placed to each other at a distance of 8 cm between them. The magnitude of magnetic field produced at mid-point between the two conductors due to current flowing in them is 300 $\mu$T. The equal current flowing in the two conductors is :

Options:

A) 30A in the same direction.

B) 30A in the opposite direction.

C) 60A in the opposite direction.

D) 300A in the opposite direction.

135

EasyJEE Mains2024

The magnetic potential due to a magnetic dipole at a point on its axis situated at a distance of $20 \mathrm{~cm} from its center is 1.5 \times 10^{-5} \mathrm{~T} \mathrm{~m}. The magnetic moment of the dipole is _________ A \mathrm{~m}^2. (Given : \frac{\mu_o}{4 \pi}=10^{-7} \mathrm{Tm} A^{-1}$ )

Options:

136

EasyJEE Mains2022

Given below are two statements : Statement I : The electric force changes the speed of the charged particle and hence changes its kinetic energy; whereas the magnetic force does not change the kinetic energy of the charged particle. Statement II : The electric force accelerates the positively charged particle perpendicular to the direction of electric field. The magnetic force accelerates the moving charged particle along the direction of magnetic field. In the light of the above statements, choose the most appropriate answer from the options given below :

Options:

A) Both Statement I and Statement II are correct.

B) Both Statement I and Statement II are incorrect.

C) Statement I is correct but Statement II is incorrect.

D) Statement I is incorrect but Statement II is correct.

137

MediumJEE Mains2023

A compass needle oscillates 20 times per minute at a place where the dip is $30^{\circ} and 30 times per minute where the dip is 60^{\circ}. The ratio of total magnetic field due to the earth at two places respectively is \frac{4}{\sqrt{x}}. The value of x$ is

Options:

138

EasyJEE Mains2022

A charge particle moves along circular path in a uniform magnetic field in a cyclotron. The kinetic energy of the charge particle increases to 4 times its initial value. What will be the ratio of new radius to the original radius of circular path of the charge particle :

Options:

A) 1 : 1

B) 1 : 2

C) 2 : 1

D) 1 : 4

139

EasyJEE Mains2023

The current required to be passed through a solenoid of 15 cm length and 60 turns in order of demagnetise a bar magnet of magnetic intensity $2.4\times10^3~Am^{-1}$ is ___________ A.

Options:

140

EasyJEE Mains2022

Two parallel, long wires are kept 0.20 m apart in vacuum, each carrying current of x A in the same direction. If the force of attraction per meter of each wire is 2 $\times 10-$6 N, then the value of x is approximately :

Options:

A) 1

B) 2.4

C) 1.4

D) 2

141

EasyJEE Mains2023

The magnetic intensity at the center of a long current carrying solenoid is found to be $1.6 \times 10^{3} \mathrm{Am}^{-1}$. If the number of turns is 8 per cm, then the current flowing through the solenoid is __________ A.

Options:

142

MediumJEE Mains2022

An infinitely long hollow conducting cylinder with radius R carries a uniform current along its surface. Choose the correct representation of magnetic field (B) as a function of radial distance (r) from the axis of cylinder.

Options:

143

EasyJEE Mains2021

In a uniform magnetic field, the magnetic needle has a magnetic moment 9.85 $\times 10-2 A/m2 and moment of inertia 5 \times 10-6 kg m2. If it performs 10 complete oscillations in 5 seconds then the magnitude of the magnetic field is _______________ mT. [Take \pi$2 as 9.85]

Options:

144

MediumJEE Mains2022

Two long parallel conductors S1 and S2 are separated by a distance 10 cm and carrying currents of 4A and 2A respectively. The conductors are placed along x-axis in X-Y plane. There is a point P located between the conductors (as shown in figure). A charge particle of 3$\pi coulomb is passing through the point P with velocity \overrightarrow v = (2\widehat i + 3\widehat j) m/s; where \widehat i and \widehat j represents unit vector along x & y axis respectively. The force acting on the charge particle is 4\pi \times {10^{ - 5}}( - x\widehat i + 2\widehat j)$ N. The value of x is :

Options:

A) 2

B) 1

C) 3

D) -$3

145

MediumJEE Mains2021

The value of aluminium susceptibility is 2.2 $\times 10-5. The percentage increase in the magnetic field if space within a current carrying toroid is filled with aluminium is {x \over {{{10}^4}}}$. Then the value of x is _________________.

Options:

146

EasyJEE Mains2022

A proton and an alpha particle of the same velocity enter in a uniform magnetic field which is acting perpendicular to their direction of motion. The ratio of the radii of the circular paths described by the alpha particle and proton is :

Options:

A) 1 : 4

B) 4 : 1

C) 2 : 1

D) 1 : 2

147

MediumJEE Mains2025

A bar magnet has total length 2 l=20 units and the field point P is at a distance \mathrm{d}=10 units from the centre of the magnet. If the relative uncertainty of length measurement is 1 \%, then uncertainty of the magnetic field at point P is :

Options:

A) 10%

B) 5%

C) 3%

D) 4%

148

EasyJEE Mains2022

A long solenoid carrying a current produces a magnetic field B along its axis. If the current is doubled and the number of turns per cm is halved, the new value of magnetic field will be equal to

Options:

A) B

B) 2B

C) 4B

D) {B \over 2}

149

MediumJEE Mains2022

A long straight wire with a circular cross-section having radius R, is carrying a steady current I. The current I is uniformly distributed across this cross-section. Then the variation of magnetic field due to current I with distance r (r < R) from its centre will be :

Options:

A) B $\propto$ r2

B) B $\propto$ r

C) B $\propto {1 \over {{r^2}}}

D) B $\propto {1 \over {{r}}}

150

MediumJEE Mains2022

A proton, a deutron and an $\alpha$-particle with same kinetic energy enter into a uniform magnetic field at right angle to magnetic field. The ratio of the radii of their respective circular paths is :

Options:

A) 1 : $\sqrt 2 : \sqrt 2

B) 1 : 1 : $\sqrt 2

C) \sqrt 2 $ : 1 : 1

D) 1 : $\sqrt 2 $ : 1

151

EasyJEE Mains2022

Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : In an uniform magnetic field, speed and energy remains the same for a moving charged particle. Reason (R) : Moving charged particle experiences magnetic force perpendicular to its direction of motion.

Options:

A) Both (A) and (R) are true and (R) is the correct explanation of (A).

B) Both (A) and (R) are true but (R) is NOT the correct explanation of (A).

C) (A) is true but (R) is false.

D) (A) is false but (R) is true.

152

EasyJEE Mains2022

The magnetic field at the centre of a circular coil of radius r, due to current I flowing through it, is B. The magnetic field at a point along the axis at a distance ${r \over 2}$ from the centre is :

Options:

A) B/2

B) 2B

C) {\left( {{2 \over {\sqrt 5 }}} \right)^3}B

D) {\left( {{2 \over {\sqrt 3}}} \right)^3}B

153

HardJEE Mains2021

There are two infinitely long straight current carrying conductors and they are held at right angles to each other so that their common ends meet at the origin as shown in the figure given below. The ratio of current in both conductor is 1 : 1. The magnetic field at point P is ____________.

Options:

A) {{{\mu _0}I} \over {4\pi xy}}\left[ {\sqrt {{x^2} + {y^2}} + (x + y)} \right]

B) {{{\mu _0}I} \over {4\pi xy}}\left[ {\sqrt {{x^2} + {y^2}} - (x + y)} \right]

C) {{{\mu _0}Ixy} \over {4\pi }}\left[ {\sqrt {{x^2} + {y^2}} - (x + y)} \right]

D) {{{\mu _0}Ixy} \over {4\pi }}\left[ {\sqrt {{x^2} + {y^2}} + (x + y)} \right]

154

MediumJEE Mains2021

A current of 1.5 A is flowing through a triangle, of side 9 cm each. The magnetic field at the centroid of the triangle is :(Assume that the current is flowing in the clockwise direction.)

Options:

A) 3 $\times 10-$7 T, outside the plane of triangle

B) 2\sqrt 3 \times 10-$7 T, outside the plane of triangle

C) 2\sqrt 3 \times 10-$5 T, inside the plane of triangle

D) 3 $\times 10-$5 T, inside the plane of triangle

155

MediumJEE Mains2021

A coil having N turns is wound tightly in the form of a spiral with inner and outer radii 'a' and 'b' respectively. Find the magnetic field at centre, when a current I passes through coil:

Options:

A) {{{\mu _0}IN} \over {2(b - a)}}{\log _e}\left( {{b \over a}} \right)

B) {{{\mu _0}I} \over 8}\left[ {{{a + b} \over {a - b}}} \right]

C) {{{\mu _0}I} \over {4(a - b)}}\left[ {{1 \over a} - {1 \over b}} \right]

D) {{{\mu _0}I} \over 8}\left( {{{a - b} \over {a + b}}} \right)

156

MediumJEE Mains2021

A coaxial cable consists of an inner wire of radius 'a' surrounded by an outer shell of inner and outer radii 'b' and 'c' respectively. The inner wire carries an electric current i0, which is distributed uniformly across cross-sectional area. The outer shell carries an equal current in opposite direction and distributed uniformly. What will be the ratio of the magnetic field at a distance x from the axis when (i) x < a and (ii) a < x < b ?

Options:

A) {{{x^2}} \over {{a^2}}}

B) {{{a^2}} \over {{x^2}}}

C) {{{x^2}} \over {{b^2} - {a^2}}}

D) {{{b^2} - {a^2}} \over {{x^2}}}

157

MediumJEE Mains2021

Two ions of masses 4 amu and 16 amu have charges +2e and +3e respectively. These ions pass through the region of constant perpendicular magnetic field. The kinetic energy of both ions is same. Then :

Options:

A) lighter ion will be deflected less than heavier ion

B) lighter ion will be deflected more than heavier ion

C) both ions will be deflected equally

D) no ion will be deflected

158

MediumJEE Mains2021

The fractional change in the magnetic field intensity at a distance 'r' from centre on the axis of current carrying coil of radius 'a' to the magnetic field intensity at the centre of the same coil is : (Take r < a)

Options:

A) {3 \over 2}{{{a^2}} \over {{r^2}}}

B) {2 \over 3}{{{a^2}} \over {{r^2}}}

C) {2 \over 3}{{{r^2}} \over {{a^2}}}

D) {3 \over 2}{{{r^2}} \over {{a^2}}}

159

MediumJEE Mains2021

Figure A and B shown to long straight wires of circular cross-section (a and b with a < b), carrying current I which is uniformly distributed across the cross-section. The magnitude of magnetic field B varies with radius r and can be represented as :

Options:

160

EasyJEE Mains2021

Two ions having same mass have charges in the ratio 1 : 2. They are projected normally in a uniform magnetic field with their speeds in the ratio 2 : 3. The ratio of the radii of their circular trajectories is :

Options:

A) 1 : 4

B) 4 : 3

C) 3 : 1

D) 2 : 3

161

MediumJEE Mains2021

A deuteron and an alpha particle having equal kinetic energy enter perpendicularly into a magnetic field. Let rd and r$\alpha be their respective radii of circular path. The value of {{{r_d}} \over {{r_\alpha }}}$ is equal to :

Options:

A) 1

B) 2

C) \sqrt 2

D) {1 \over {\sqrt 2 }}

162

MediumJEE Mains2021

A proton and an $\alpha-particle, having kinetic energies Kp and K\alpha respectively, enter into a magnetic field at right angles.The ratio of the radii of trajectory of proton to that of \alpha-particle is 2 : 1. The ratio of Kp : K\alpha$ is :

Options:

A) 8 : 1

B) 4 : 1

C) 1 : 8

D) 1 : 4

163

MediumJEE Mains2021

Four identical long solenoids A, B, C and D are connected to each other as shown in the figure. If the magnetic field at the center of A is 3T, the field at the center of C would be : (Assume that the magnetic field is confined with in the volume of respective solenoid).

Options:

A) 12T

B) 6T

C) 9T

D) 1T

164

MediumJEE Mains2021

A loop of flexible wire of irregular shape carrying current is placed in an external magnetic field. Identify the effect of the field on the wire.

Options:

A) Loop assumes circular shape with its plane normal to the field.

B) Loop assumes circular shape with its plane parallel to the field.

C) Wire gets stretched to become straight.

D) Shape of the loop remains unchanged.

165

MediumJEE Mains2021

A hairpin like shape as shown in figure is made by bending a long current carrying wire. What is the magnitude of a magnetic field at point P which lies on the centre of the semicircle?

Options:

A) {{{\mu _0}I} \over {4\pi r}}(2 - \pi )

B) {{{\mu _0}I} \over {2\pi r}}(2 - \pi )

C) {{{\mu _0}I} \over {4\pi r}}(2 + \pi )

D) {{{\mu _0}I} \over {2\pi r}}(2 + \pi )

166

MediumJEE Mains2021

A solenoid of 1000 turns per metre has a core with relative permeability 500. Insulated windings of the solenoid carry an electric current of 5A. The magnetic flux density produced by the solenoid is : (permeability of free space = 4$\pi \times 10-$7 H/m)

Options:

A) \pi$T

B) 2 $\times 10-3\pi$ T

C) 10$-4\pi$ T

D) {\pi \over 5}$ T

167

EasyJEE Mains2021

A charge Q is moving $\overrightarrow {dl} distance in the magnetic field \overrightarrow {B} . Find the value of work done by \overrightarrow {B} $.

Options:

A) Zero

B) -$1

C) Infinite

D) 1

168

MediumJEE Mains2021

A proton, a deuteron and an $\alpha$ particle are moving with same momentum in a uniform magnetic field. The ratio of magnetic forces acting on them is ___ and their speed is _, in the ratio.

Options:

A) 2 : 1 : 1 and 4 : 2 : 1

B) 4 : 2 : 1 and 2 : 1 : 1

C) 1 : 2 : 4 and 2 : 1 : 1

D) 1 : 2 : 4 and 1 : 1 : 2

169

MediumJEE Mains2021

Magnetic fields at two points on the axis of a circular coil at a distance of 0.05 m and 0.2 m from the centre are in the ratio 8 : 1. The radius of coil is ________.

Options:

A) 1.0 m

B) 0.15 m

C) 0.2 m

D) 0.1 m

170

MediumJEE Mains2020

A square loop of side 2$a$ and carrying current I is kept in xz plane with its centre at origin. A long wire carrying the same current I is placed parallel to z-axis and passing through point (0, b, 0), (b >> a). The magnitude of torque on the loop about z-axis will be :

Options:

A) {{2{\mu _0}{I^2}{a^2}} \over {\pi b}}

B) {{2{\mu _0}{I^2}{a^2}b} \over {\pi \left( {{a^2} + {b^2}} \right)}}

C) {{{\mu _0}{I^2}{a^2}b} \over {2\pi \left( {{a^2} + {b^2}} \right)}}

D) {{{\mu _0}{I^2}{a^2}} \over {2\pi b}}

171

MediumJEE Mains2020

A charged particle going around in a circle can be considered to be a current loop. A particle of mass m carrying charge q is moving in a plane with speed v under the influence of magnetic field $\overrightarrow B $. The magnetic moment of this moving particle:

Options:

A) {{m{v^2}\overrightarrow B } \over {2{B^2}}}

B) -${{m{v^2}\overrightarrow B } \over {2{B^2}}}

C) -${{m{v^2}\overrightarrow B } \over {{B^2}}}

D) -${{m{v^2}\overrightarrow B } \over {2\pi {B^2}}}

172

MediumJEE Mains2020

A particle of charge q and mass m is moving with a velocity $ - v\widehat i (v \ne 0) towards a large screen placed in the Y - Z plane at a distance d. If there is a magnetic field \overrightarrow B = {B_0}\widehat k$ , the maximum value of v for which the particle will not hit the screen is :

Options:

A) {{2qd{B_0}} \over m}

B) {{qd{B_0}} \over {3m}}

C) {{qd{B_0}} \over {2m}}

D) {{qd{B_0}} \over {m}}

173

MediumJEE Mains2020

An electron is moving along +x direction with a velocity of 6 $ \times $ 106 ms–1. It enters a region of uniform electric field of 300 V/cm pointing along +y direction. The magnitude and direction of the magnetic field set up in this region such that the electron keeps moving along the x direction will be :

Options:

A) 3 $ \times $ 10–4 T, along –z direction

B) 5 $ \times $ 10–3 T, along –z direction

C) 5 $ \times $ 10–3 T, along +z direction

D) 3 $ \times $ 10–4 T, along +z direction

174

MediumJEE Mains2020

An iron rod of volume 10–3 m3 and relative permeability 1000 is placed as core in a solenoid with 10 turns/cm. If a current of 0.5 A is passed through the solenoid, then the magnetic moment of the rod will be :

Options:

A) 5 $ \times $ 102 Am2

B) 0.5 $ \times $ 102 Am2

C) 500 $ \times $ 102 Am2

D) 50 $ \times $ 102 Am2

175

MediumJEE Mains2020

A square loop of side 2$a$, and carrying current I, is kept in XZ plane with its centre at origin. A long wire carrying the same current I is placed parallel to the z-axis and passing through the point (0, b, 0), (b >> a). The magnitude of the torque on the loop about zaxis is given by :

Options:

A) {{2{\mu _0}{I^2}{a^2}} \over {\pi b}}

B) {{{\mu _0}{I^2}{a^2}} \over {2\pi b}}

C) {{{\mu _0}{I^2}{a^3}} \over {2\pi {b^2}}}

D) {{2{\mu _0}{I^2}{a^3}} \over {\pi {b^2}}}

176

MediumJEE Mains2020

A circular coil has moment of inertia 0.8 kg m2 around any diameter and is carrying current to produce a magnetic moment of 20 Am2 . The coil is kept initially in a vertical position and it can rotate freely around a horizontal diameter. When a uniform magnetic field of 4 T is applied along the vertical,it starts rotating around its horizontal diameter. The angular speed the coil acquires after rotating by 60o will be:

Options:

A) 10 $\pi $ rad s–1

B) 20 $\pi $ rad s–1

C) 10{\left( 3 \right)^{1/4}}$ rad s–1

D) 20 rad s–1

177

MediumJEE Mains2020

A wire A, bent in the shape of an arc of a circle, carrying a current of 2 A and having radius 2 cm and another wire B, also bent in the shape of arc of a circle, carrying a current of 3 A and having radius of 4 cm, are placed as shown in the figure. The ratio of the magnetic fields due to the wires A and B at the common centre O is :

Options:

A) 4 : 6

B) 6 : 4

C) 2 : 5

D) 6 : 5

178

MediumJEE Mains2020

Magnitude of magnetic field (in SI units) at the centre of a hexagonal shape coil of side 10 cm, 50 turns and carrying current I (Ampere) in units of ${{{\mu _0}I} \over \pi }$ is :

Options:

A) 250$\sqrt 3

B) 5$\sqrt 3

C) 500$\sqrt 3

D) 50$\sqrt 3

179

MediumJEE Mains2020

A charged particle carrying charge 1 $\mu C is moving with velocity \left( {2\widehat i + 3\widehat j + 4\widehat k} \right) ms–1. If an external magnetic field of \left( {5\widehat i + 3\widehat j - 6\widehat k} \right)× 10–3 T exists in the region where the particle is moving then the force on the particle is \overrightarrow F × 10–9 N. The vector \overrightarrow F $ is :

Options:

A) { - 0.30\widehat i + 0.32\widehat j - 0.09\widehat k}

B) { - 300\widehat i + 320\widehat j - 90\widehat k}

C) { - 30\widehat i + 32\widehat j - 9\widehat k}

D) { - 3.0\widehat i + 3.2\widehat j - 0.9\widehat k}

180

MediumJEE Mains2020

A wire carrying current I is bent in the shape ABCDEFA as shown, where rectangle ABCDA and ADEFA are perpendicular to each other. If the sides of the rectangles are of lengths a and b, then the magnitude and direction of magnetic moment of the loop ABCDEFA is

Options:

A) \sqrt 2 abI, along \left( {{{\widehat j} \over {\sqrt 5 }} + {{2\widehat k} \over {\sqrt 5 }}} \right)

B) abI, along $\left( {{{\widehat j} \over {\sqrt 5 }} + {{2\widehat k} \over {\sqrt 5 }}} \right)

C) \sqrt 2 abI, along \left( {{{\widehat j} \over {\sqrt 2 }} + {{\widehat k} \over {\sqrt 2 }}} \right)

D) abI, along $\left( {{{\widehat j} \over {\sqrt 2 }} + {{\widehat k} \over {\sqrt 2 }}} \right)

181

MediumJEE Mains2020

The figure shows a region of length ‘l’ with a uniform magnetic field of 0.3 T in it and a proton entering the region with velocity 4 $ \times 105 ms–1 making an angle 60o with the field. If the proton completes 10 revolution by the time it cross the region shown, ‘l’ is close to (mass of proton = 1.67 \times 10–27 kg, charge of the proton = 1.6 \times $ 10–19 C)

Options:

A) 0.22 m

B) 0.11 m

C) 0.88 m

D) 0.44 m

182

MediumJEE Mains2020

A beam of protons with speed 4 × 105 ms–1 enters a uniform magnetic field of 0.3 T at an angle of 60° to the magnetic field. The pitch of the resulting helical path of protons is close to : (Mass of the proton = 1.67 $ \times 10–27 kg, charge of the proton = 1.69 \times $ 10–19 C)

Options:

A) 2 cm

B) 12 cm

C) 5 cm

D) 4 cm

183

MediumJEE Mains2020

An electron gun is placed inside a long solenoid of radius R on its axis. The solenoid has n turns/length and carries a current I. The electron gun shoots an electron along the radius of the solenoid with speed v. If the electron does not hit the surface of the solenoid, maximum possible value of v is (all symbols have their standard meaning) :

Options:

A) {{e{\mu _0}nIR} \over {4m}}

B) {{e{\mu _0}nIR} \over m}

C) {{e{\mu _0}nIR} \over {2m}}

D) {{2e{\mu _0}nIR} \over m}

184

MediumJEE Mains2020

A small circular loop of conducting wire has radius a and carries current I. It is placed in a uniform magnetic field B perpendicular to its plane such that when rotated slightly about its diameter and released, it starts performing simple harmonic motion of time period T. If the mass of the loop is m then :

Options:

A) T = \sqrt {{{2m} \over {IB}}}

B) T = \sqrt {{{\pi m} \over {IB}}}

C) T = \sqrt {{{\pi m} \over {2IB}}}

D) T = \sqrt {{{2\pi m} \over {IB}}}

185

MediumJEE Mains2020

A long, straight wire of radius a carries a current distributed uniformly over its cross-section. The ratio of the magnetic fields due to the wire at distance ${a \over 3} and 2a$, respectively from the axis of the wire is :

Options:

A) 2

B) {1 \over 2}

C) {3 \over 2}

D) {2 \over 3}

186

MediumJEE Mains2020

A charged particle of mass 'm' and charge 'q' moving under the influence of uniform electric field $E\overrightarrow i and a uniform magnetic field B\overrightarrow k follows a trajectory from point P to Q as shown in figure. The velocities at P and Q are respectively, v\overrightarrow i and - 2v\overrightarrow j . Then which of the following statements (A, B, C, D) are the correct ? (Trajectory shown is schematic and not to scale) : (A) E = {3 \over 4}\left( {{{m{v^2}} \over {qa}}} \right) (B) Rate of work done by the electric field at P is {3 \over 4}\left( {{{m{v^3}} \over a}} \right)$ (C) Rate of work done by both the fields at Q is zero (D) The difference between the magnitude of angular momentum of the particle at P and Q is 2mav.

Options:

A) (A), (B), (C), (D)

B) (A), (B), (C)

C) (A), (C), (D)

D) (B), (C), (D)

187

MediumJEE Mains2020

A very long wire ABDMNDC is shown in figure carrying current I. AB and BC parts are straight, long and at right angle. At D wire forms a circular turn DMND of radius R. AB, BC parts are tangential to circular turn at N and D. Magnetic field at the centre of circle is :

Options:

A) {{{\mu _0}I} \over {2\pi R}}\left( {\pi + 1} \right)

B) {{{\mu _0}I} \over {2\pi R}}\left( {\pi - {1 \over {\sqrt 2 }}} \right)

C) {{{\mu _0}I} \over {2R}}

D) {{{\mu _0}I} \over {2\pi R}}\left( {\pi + {1 \over {\sqrt 2 }}} \right)

188

MediumJEE Mains2020

Photon with kinetic energy of 1MeV moves from south to north. It gets an acceleration of 1012 m/s2 by an applied magnetic field (west to east). The value of magnetic field : (Rest mass of proton is 1.6 × 10–27 kg) :

Options:

A) 0.71mT

B) 7.1mT

C) 0.071mT

D) 71mT

189

MediumJEE Mains2020

A particle of mass m and charge q has an initial velocity $\overrightarrow v = {v_0}\widehat j . If an electric field \overrightarrow E = {E_0}\widehat i and magnetic field \overrightarrow B = {B_0}\widehat i$ act on the particle, its speed will double after a time:

Options:

A) {{3m{v_0}} \over {q{E_0}}}

B) {{\sqrt 2 m{v_0}} \over {q{E_0}}}

C) {{\sqrt 3 m{v_0}} \over {q{E_0}}}

D) {{2m{v_0}} \over {q{E_0}}}

190

MediumJEE Mains2019

Find the magnetic field at point P due to a straight line segment AB of length 6 cm carrying a current of 5A. (See figure) ($\mu 0 = 4\pi $ × 10–7 N-A–2)

Options:

A) 1.5 × 10–5 T

B) 3.0 × 10–5 T

C) 2.0 × 10–5 T

D) 2.5 × 10–5 T

191

MediumJEE Mains2019

An electron, moving along the x-axis with an initial energy of 100 eV, enters a region of magnetic field $\overrightarrow B = \left( {1.5 \times {{10}^{ - 3}}T} \right)\widehat k$ at S (See figure). The field extends between x = 0 and x = 2 cm. The electron is detected at the point Q on a screen placed 8 cm away from the point S. The distance d between P and Q (on the screen) is : (electron’s charge = 1.6 × 10–19 C, mass of electron = 9.1 × 10–31 kg)

Options:

A) 2.25 cm

B) 12.87 cm

C) 1.22 cm

D) 11.65 cm

192

MediumJEE Mains2019

A thin ring of 10 cm radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of 40 $\pi rad s–1 about its axis, perpendicular to its plane. If the magnetic field at its centre is 3.8 × 10–9 T, then the charge carried by the ring is close to (\mu 0 = 4\pi $ × 10–7 N/A2 ).

Options:

A) 7 × 10–6 C

B) 4 × 10–5 C

C) 2 × 10–6 C

D) 3 × 10–5 C

193

MediumJEE Mains2019

The magnitude of the magnetic field at the centre of an equilateral triangular loop of side 1 m which is carrying a current of 10 A is : [Take $\mu 0 = 4\pi $ × 10–7 NA–2]

Options:

A) 3 $\mu $T

B) 18 $\mu $T

C) 9 $\mu $T

D) 1 $\mu $T

194

MediumJEE Mains2019

A square loop is carrying a steady current I and the magnitude of its magnetic dipole moment is m. if this square loop is changed to a circular loop and it carries the same current, the magnitude of the magnetic dipole moment of circular loop will be:

Options:

A) {m \over \pi }

B) {{3m} \over \pi }

C) {{2m} \over \pi }

D) {{4m} \over \pi }

195

MediumJEE Mains2019

Two wires A & B are carrying currents I1 & I2 as shown in the figure. The separation between them is d. A third wire C carrying a current I is to be kept parallel to them at a distance x from A such that the net force acting on it is zero. The possible values of x are :

Options:

A) x = \left( {{{{I_1}} \over {{I_1} + {I_2}}}} \right)d\,and\,x = \left( {{{{I_2}} \over {{I_1} - {I_2}}}} \right)d

B) x = \left( {{{{I_2}} \over {{I_1} + {I_2}}}} \right)d\,and\,x = \left( {{{{I_2}} \over {{I_1} - {I_2}}}} \right)d

C) x = \left( {{{{I_1}} \over {{I_1} - {I_2}}}} \right)d\,and\,x = \left( {{{{I_2}} \over {{I_1} + {I_2}}}} \right)d

D) x = \pm {{{I_1}d} \over {{I_1} - {I_2}}}

196

MediumJEE Mains2019

A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbits in a plane due to magnetic field perpendicualr to the plane. Let rp, re and rHe be their respective radii, then

Options:

A) re < rp < rHe

B) re < rp = rHe

C) re > rp > rHe

D) re > rp = rHe

197

MediumJEE Mains2019

A moving coil galvanometer has a coil with 175 turns and area 1 cm2. It uses a torsion band of torsion constant 10–6 N-m/rad. The coil is placed in a maganetic field B parallel to its plane. The coil deflects by 1° for a current of 1 mA. The value of B (in Tesla) is approximately :-

Options:

A) 10–4

B) 10–2

C) 10–1

D) 10–3

198

MediumJEE Mains2019

A rectangular coil (Dimension 5 cm × 2.5 cm) with 100 turns, carrying a current of 3 A in the clock-wise direction is kept centered at the origin and in the X-Z plane. A magnetic field of 1 T is applied along X-axis. If the coil is tilted through 45° about Z-axis, then the torque on the coil is :

Options:

A) 0.42 Nm

B) 0.55 Nm

C) 0.38 Nm

D) 0.27 Nm

199

MediumJEE Mains2019

A rigid square loop of side 'a' and carrying current I2 is lying on a horizontal surface near a long current I1 carrying wire in the same plane as shown in figure. The net force on the loop due to wire will be :

Options:

A) Repulsive and equal to $\mu 0I1I2/4\pi

B) Attractive and equal to $\mu 0I1I2/3\pi

C) Repulsive and equal to $\mu 0I1I2/2\pi

D) Zero

200

MediumJEE Mains2019

Two very long, straight, and insulated wires are kept at 90° angle from each other in xy-plane as shown in the figure. These wires carry currents of equal magnitude I, whose directions are shown in the figure. The net magnetic field at point P will be :

Options:

A) {{ + {\mu _0}I} \over {\pi d}}\left( {\mathop z\limits^ \wedge } \right)

B) - {{{\mu _0}I} \over {2\pi d}}\left( {\mathop x\limits^ \wedge + \mathop y\limits^ \wedge } \right)

C) Zero

D) {{{\mu _0}I} \over {2\pi d}}\left( {\mathop x\limits^ \wedge + \mathop y\limits^ \wedge } \right)

201

MediumJEE Mains2019

A thin strip 10 cm long is on a U shaped wire of negligible resistance and it is connected to a spring of spring constant 0.5 Nm–1 (see figure). The assembly is kept in a uniform magnetic field of 0.1 T. If the strip is pulled from its equilibrium position and released, the number of oscillation it performs before its amplitude decreases by a factor of e is N. If the mass of the strip is 50 grams, its resistance 10W and air drag negligible, N will be close to :

Options:

A) 50000

B) 1000

C) 5000

D) 10000

202

MediumJEE Mains2019

A circular coil having N turns and radius r carries a current I. It is held in the XZ plane in a magnetic field B${\mathop i\limits^ \wedge }$ . The torque on the coil due to the magnetic field is :

Options:

A) {{B{r^2}I} \over {\pi N}}

B) B$\pi $r2IN

C) Zero

D) {{B\pi{r^2}I} \over { N}}

203

MediumJEE Mains2019

A proton and an $\alpha -particle (with their masses in the ratio of 1 : 4 and charges in the ratio of 1 : 2) are accelerated from rest through a potential difference V. If a uniform magnetic field (B) is set up perpendicular to their velocities, the ratio of the radii rp : r\alpha $ of the circular paths described by them will be ;

Options:

A) 1:\sqrt 3

B) 1 : 3

C) 1:\sqrt 2

D) 1 : 2

204

MediumJEE Mains2019

As shown in the figure, two infinitely long, identical wires are bent by 90o and placed in such a way that the segments LP and QM are along the x-axis, while segments PS and QN are parallel to the y-axis. If OP = OQ = 4cm, and the magnitude of the magnetic field at O is 10–4 T, and the two wires carry equal currents (see figure), the magnitude of the current in each wire and the direction of the magnetic field at O will be ($\mu 0 = 4\pi \times $ 10–7 NA–2) :

Options:

A) 40 A, perpendicular into the page

B) 40 A, perpendicular out of the page

C) 20 A, perpendicular into the page

D) 40 A, perpendicular out of the page

205

MediumJEE Mains2019

The region between y = 0 and y = d contains a magnetic field $\overrightarrow B = B\widehat z. A particle of mass m and charge q enters the region with a velocity \overrightarrow v = v\widehat i. If d = {{mv} \over {2qB}},$ the acceleration of the charged particle at the point of its emergence at the other side is :

Options:

A) {{qvB} \over m}\left( -{{{\sqrt 3 } \over 2}\widehat i - {1 \over 2}\widehat j} \right)

B) {{qvB} \over m}\left( {{1 \over 2}\widehat i - {{\sqrt 3 } \over 2}\widehat j} \right)

C) {{qvB} \over m}\left( {{{ - \widehat j + \widehat i} \over {\sqrt 2 }}} \right)

D) {{qvB} \over m}\left( {{{\widehat j + \widehat i} \over {\sqrt 2 }}} \right)

206

MediumJEE Mains2019

A particle of mass m and charge q is in an electric and magnetic field given by $\overrightarrow E = 2\widehat i + 3\widehat j;\,\,\,\overrightarrow B = 4\widehat j + 6\widehat k.$ The charged particle is shifted from he origin to the point P(x = 1; y = 1) along a straight path. The magnitude of the total work done is :

Options:

A) (2.5) q

B) (0.35) q

C) (0.15) q

D) 5 q

207

MediumJEE Mains2019

In an experiment, electrons are accelerated, from rest, by applying a voltage of 500 V. Calculate the radius of the path if a magnetic field 100 mT is then applied. [Charge of the electron = 1.6 $ \times 10–19 C Mass of the electron = 9.1 \times $ 10–31 kg]

Options:

A) 7.5 $ \times 10-$4 m

B) 7.5 $ \times 10-$3 m

C) 7.5 m

D) 7.5 $ \times 10-$2 m

208

MediumJEE Mains2019

A hoop and a solid cylinder of same mass and radius are made of a permanent magnetic material with their magnetic moment parallel to their respective axes. But the magnetic moment of hoop is twice of solid cylinder. They are placed in a uniform magnetic field in such a manner that their magnetic moments make a small angle with the field. If the oscillation periods of hoop and cylinder are Th and Tc respectively, then -

Options:

A) Th = 1.5 Tc

B) Th = Tc

C) Th = 2Tc

D) Th = 0.5 Tc

209

MediumJEE Mains2019

An insulating thin rod of length $l has a linear charge density \rho \left( x \right) = {\rho _0}{x \over l}$ on it. The rod is rotated about an axis passing through the origin (x = 0) and perpendicular to the rod. If the rod makes n rotations per second, then the time averaged magnetic moment of the rod is -

Options:

A) {\pi \over 3}n\rho {l^3}

B) {\pi \over 4}n\rho {l^3}

C) n\rho {l^3}

D) \pi n\rho {l^3}

210

MediumJEE Mains2019

A particle having the same charge as of electron moves in a ciurcular path of radius 0.5 cm under the influence of a magnetic field 0f 0.5 T. If an electric field of 100 V/m makes it to move in a straight path, then the mass of the particle is (Given charge of electron = 1.6 $ \times 10-$19C)

Options:

A) 9.1 $ \times 10-$31 kg

B) 1.6 $ \times 10-$27 kg

C) 1.6 $ \times 10-$19 kg

D) 2.0 $ \times 10-$24 kg

211

MediumJEE Mains2019

One of the two identical conducting wires of length L is bent in the form of a circular loop and the other one into a circular coil of N identical turns. If the same current is passed in both, the radio of the magnetic field at the central of the loop (BL) to that at the center of the coil (BC), i.e. ${{{B_L}} \over {{B_C}}}$ will be :

Options:

A) N

B) {1 \over N}

C) N2

D) {1 \over {{N^2}}}

212

MediumJEE Mains2019

A current loop, having two circular arcs joined by two radial lines is shown in the figure. It carries a current of 10 A. The magnetic field at point O will be close to :

Options:

A) 1.0 $ \times 10-$7 T

B) 1.5 $ \times 10-$7 T

C) 1.5 $ \times 10-$5 T

D) 1.0 $ \times 10-$5 T

213

MediumJEE Mains2019

An infinitely long current carrying wire and a small current carrying loop are in the plane of the paper as shown. The radius of the loop is a and distance of its centre from the wire is d (d > > a). If the loop a applies a force F on the wire then :

Options:

A) F = 0

B) F \propto \left( {{a \over d}} \right)

C) F \propto \left( {{{{a^2}} \over {{d^3}}}} \right)

D) F \propto {\left( {{a \over d}} \right)^2}

214

MediumJEE Mains2018

A charge q is spread uniformly over an insulated loop of radius r. If it is rotated with an angular velocity $\omega $ with resect to normal axis then the magnetic moment of the loop is :

Options:

A) q $\omega $r2

B) {4 \over 3} q \omega $r2

C) {3 \over 2} q \omega $r2

D) {1 \over 2} q \omega $r2

215

MediumJEE Mains2018

An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii re, rp, r$_\alpha respectively in a uniform magnetic field B. The relation between re, rp, r_\alpha$ is:

Options:

A) re < r$_\alpha$ < rp

B) re > rp = r$_\alpha

C) re < rp = r$_\alpha

D) re < rp < r$_\alpha

216

MediumJEE Mains2018

The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the loop is B1. When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is ${{B_2}}. The ratio {{{B_1}} \over {{B_2}}}$ is:

Options:

A) 2

B) \sqrt 3

C) \sqrt 2

D) 1 \over \sqrt 2

217

MediumJEE Mains2018

A current of 1 A is flowing on the sides of an equilateral triangle of side 4.5 $ \times $ 10-2 m. The magnetic field at the center of the triangle will be :

Options:

A) 2 $ \times $ 10-5 Wb/m2

B) Zero

C) 8 $ \times $ 10-5 Wb/m2

D) 4 $ \times $ 10-5 Wb/m2

218

MediumJEE Mains2018

A Helmholtz coil has a pair of loops, each with $N turns and radius R. They are placed coaxially at distance R and the same current {\rm I} flows through the loops in the same direction. P, midway between the centers A and C$, is given by [Refer to figure given below] :

Options:

A) {{8N{\mu _0}{\rm I}} \over {{5^{1/2}}R}}

B) {{8N{\mu _0}{\rm I}} \over {{5^{3/2}}R}}

C) {{4N{\mu _0}{\rm I}} \over {{5^{1/2}}R}}

D) {{4N{\mu _0}{\rm I}} \over {{5^{3/2}}R}}

219

MediumJEE Mains2017

A negative test charge is moving near a long straight wire carrying a current. The force acting on the test charge is parallel to the direction of the current. The motion of the charge is :

Options:

A) away from the wire

B) towards the wire

C) parallel to the wire along the current

D) parallel to the wire opposite to the current

220

MediumJEE Mains2017

A magnetic dipole in a constant magnetic field has :

Options:

A) maximum potential energy when the torque is maximum.

B) zero potential energy when the torque is minimum.

C) zero potential energy when the torque is maximum.

D) minimum potential energy when the torque is maximum.

221

MediumJEE Mains2017

In a certain region static electric and magnetic fields exist. The magnetic field is given by $\overrightarrow B = {B_0}\left( {\widehat i + 2\widehat j - 4\widehat k} \right) . If a test charge moving with a velocity \overrightarrow \upsilon = {\upsilon _0}\left( {3\widehat i - \widehat j + 2\widehat k} \right)$ experiences no force in that region, then the electric field in the region, in SI units, is :

Options:

A) \overrightarrow E = - {\upsilon _0}\,{B_0}\left( {3\widehat i - 2\widehat j - 4\widehat k} \right)

B) \overrightarrow E = - {\upsilon _0}\,{B_0}\left( {\widehat i + \widehat j + 7\widehat k} \right)

C) \overrightarrow E = {\upsilon _0}\,{B_0}\left( {14\widehat j + 7\widehat k} \right)

D) \overrightarrow E = - {\upsilon _0}\,{B_0}\left( {14\widehat j + 7\widehat k} \right)

222

MediumJEE Mains2016

To know the resistance G of a galvanometer by half deflection method, a battery of emf VE and resistance R is used to deflect the galvanometer by angle $\theta $. If a shunt of resistance S is needed to get half deflection then G, R and S are related by the equation :

Options:

A) 2S (R + G) = RG

B) S (R + G) = RG

C) 2S = G

D) 2G = S

223

MediumJEE Mains2016

A magnetic dipole is acted upon by two magnetic fields which are inclined to each other at an angle of 75o. One of the fields has a magnitude of 15 mT. The dipole attains stable equilibrium at an angle of 30o with this field. The magnitude of the other field (in mT ) is close to

Options:

A) 11

B) 36

C) 1

D) 1060

224

MediumJEE Mains2016

Two identical wires $A and B, each of length 'l', carry the same current I. Wire A is bent into a circle of radius R and wire B is bent to form a square of side 'a'. If {B_A} and {B_B} are the values of magnetic fields at the centres of the circle and square respectively, then the ratio {{{B_A}} \over {{B_B}}}$ is:

Options:

A) {{{\pi ^2}} \over {16}}

B) {{{\pi ^2}} \over {8\sqrt 2 }}

C) {{{\pi ^2}} \over {8}}

D) {{{\pi ^2}} \over {16\sqrt 2 }}

225

MediumJEE Mains2015

Two long current carrying thin wires, both with current $I, are held by insulating threads of length L and are in equilibrium as shown in the figure, with threads making an angle '\theta ' with the vertical. If wires have mass \lambda per unit-length then the value of I is : (g= gravitational acceleration$ )

Options:

A) 2\sqrt {{{\pi gL} \over {{\mu _0}}}\tan \theta }

B) \sqrt {{{\pi \lambda gL} \over {{\mu _0}}}\tan \theta }

C) \sin \theta \sqrt {{{\pi \lambda gL} \over {{\mu _0}\,\cos \theta }}}

D) 2\sin \theta \sqrt {{{\pi \lambda gL} \over {{\mu _0}\,\cos \theta }}}

226

MediumJEE Mains2015

A rectangular loop of sides $10 cm and 5 cm carrying a current 1 of 12A is placed in different orientations as shown in the figures below : If there is a uniform magnetic field of 0.3 T in the positive z direction, in which orientations the loop would be in (i) stable equilibrium and (ii)$ unstable equilibrium ?

Options:

A) (B) and (D)$, respectively

B) (B) and (C)$, respectively

C) (A) and (B)$, respectively

D) (A) and (C)$, respectively

227

MediumJEE Mains2014

A conductor lies along the $z-axis at - 1.5 \le z < 1.5\,m and carries a fixed current of 10.0 A in - {\widehat a_z} direction (see figure). For a field \overrightarrow B = 3.0 \times {10^{ - 4}}\,{e^{ - 0.2x}}\,\,{\widehat a_y}\,\,T, find the power required to move the conductor at constant speed to x=2.0 m, y=0 m in 5 \times {10^{ - 3}}s. Assume parallel motion along the x$-axis.

Options:

A) 1.57W

B) 2.97W

C) 14.85 W

D) 29.7W

228

MediumJEE Mains2012

A charge $Q is uniformly distributed over the surface of non-conducting disc of radius R. The disc rotates about an axis perpendicular to its plane and passing through its center with an angular velocity \omega . As a result of this rotation a magnetic field of induction B$ is obtained at the center of the disc. If we keep both the amount of charge placed on the disc and its angular velocity to be constant and very the radius of the disc then the variation of the magnetic induction at the center of the disc will be represented by the figure :

Options:

229

MediumJEE Mains2012

Proton, deuteron and alpha particle of same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, denuteron and alpha particle are respectively ${r_p},{r_d} and {r_\alpha }$. Which one of the following relation is correct?

Options:

A) {r_\alpha } = {r_p} = {r_d}

B) {r_\alpha } = {r_p} < {r_d}

C) {r_\alpha } > {r_d} > {r_p}

D) {r_\alpha } = {r_d} > {r_p}

230

MediumJEE Mains2011

A current $I flows in an infinitely long wire with cross section in the form of a semi-circular ring of radius R.$ The magnitude of the magnetic induction along its axis is:

Options:

A) {{{\mu _0}I} \over {2{\pi ^2}R}}

B) {{{\mu _0}I} \over {2\pi R}}

C) {{{\mu _0}I} \over {4\pi R}}

D) {{{\mu _0}I} \over {{\pi ^2}R}}

231

MediumJEE Mains2010

Two long parallel wires are at a distance $2d apart. They carry steady equal currents flowing out of the plane of the paper as shown. The variation of the magnetic field B along the line XX'$ is given by

Options:

232

MediumJEE Mains2009

A current loop $ABCD is held fixed on the plane of the paper as shown in the figure. The arcs BC (radius = b) and DA (radius =a) of the loop are joined by two straight wires AB and CD. A steady current I is flowing in the loop. Angle made by AB and CD at the origin O is {30^ \circ }. Another straight thin wire steady current {I_1} flowing out of the plane of the paper is kept at the origin. The magnitude of the magnetic field (B) due to the loop ABCD at the origin (O)$ is :

Options:

A) {{{\mu _0}I\left( {b - a} \right)} \over {24ab}}

B) {{{\mu _0}I} \over {4\pi }}\left[ {{{b - a} \over {ab}}} \right]

C) {{{\mu _0}I} \over {4\pi }}\left[ {2\left( {b - a} \right) + {\raise0.5ex\hbox{\scriptstyle \pi } \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 3}}\left( {a + b} \right)} \right]

D) zero

233

MediumJEE Mains2009

A current loop $ABCD is held fixed on the plane of the paper as shown in the figure. The arcs BC (radius = b) and DA (radius =a) of the loop are joined by two straight wires AB and CD. A steady current I is flowing in the loop. Angle made by AB and CD at the origin O is {30^ \circ }. Another straight thin wire steady current {I_1} flowing out of the plane of the paper is kept at the origin. Due to the presence of the current {I_1}$ at the origin:

Options:

A) The forces on $AD are BC$ are zero.

B) The magnitude of the net force on the loop is given by ${{{I_1}I} \over {4\pi }}{\mu _0}\left[ {2\left( {b - a} \right) + {\raise0.5ex\hbox{\scriptstyle \pi } \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 3}}\left( {a + b} \right)} \right].

C) The magnitude of the net force on the loop is given by ${{{\mu _0}I{I_1}} \over {24ab}}\left( {b - a} \right).

D) The forces on $AB and DC$ are zero.

234

MediumJEE Mains2008

A horizontal overhead powerline is at height of $4m from the ground and carries a current of 100A from east to west. The magnetic field directly below it on the ground is \left( {{\mu _0} = 4\pi \times {{10}^{ - 7}}\,\,Tm\,\,{A^{ - 1}}} \right)

Options:

A) 2.5 \times {10^{ - 7}}\,T$ southward

B) 5 \times {10^{ - 6}}\,T$ northward

C) 5 \times {10^{ - 6}}\,T$ southward

D) 2.5 \times {10^{ - 7}}\,T$ northward

235

MediumJEE Mains2007

A charged particle with charge $q enters a region of constant, uniform and mutually orthogonal fields \overrightarrow E and \overrightarrow B with a velocity \overrightarrow v perpendicular to both \overrightarrow E and \overrightarrow B, and comes out without any change in magnitude or direction of \overrightarrow v $. Then

Options:

A) \overrightarrow v = \overrightarrow B \times \overrightarrow E /{E^2}

B) \overrightarrow v = \overrightarrow E \times \overrightarrow B /{B^2}

C) \overrightarrow v = \overrightarrow B \times \overrightarrow E /{B^2}

D) \overrightarrow v = \overrightarrow E \times \overrightarrow B /{E^2}

236

MediumJEE Mains2007

A current $I$ flows along the length of an infinitely long, straight, thin walled pipe. Then

Options:

A) the magnetic field at all points inside the pipe is the same, but not zero

B) the magnetic field is zero only on the axis of the pipe

C) the magnetic field is different at different points inside the pipe

D) the magnetic field at any point inside the pipe is zero

237

MediumJEE Mains2007

A long straight wire of radius $a carries a steady current i. The current is uniformly distributed across its cross section. The ratio of the magnetic field at a/2 and 2a$ is

Options:

A) 1/2

B) 1/4

C) 4

D) 1

238

MediumJEE Mains2007

A charged particle moves through a magnetic field perpendicular to its direction. Then

Options:

A) Kinetic energy changes but the momentum is constant

B) the momentum changes but the kinetic energy is constant

C) both momentum and kinetic energy of the particle are not constant

D) both momentum and kinetic energy of the particle are constant

239

MediumJEE Mains2007

Two identical conducting wires $AOB and COD are placed at right angles to each other. The wire AOB carries an electric current {I_1} and COD carries a current {I_2}. The magnetic field on a point lying at a distance d from O, in a direction perpendicular to the plane of the wires AOB and COD$ , will be given by

Options:

A) {{{\mu _0}} \over {2\pi d}}\left( {I_1^2 + I_2^2} \right)

B) {{{\mu _0}} \over {2\pi }}{\left( {{{{I_1} + {I_2}} \over d}} \right)^{{1 \over 2}}}

C) {{{\mu _0}} \over {2\pi d}}{\left( {I_1^2 + I_2^2} \right)^{{1 \over 2}}}

D) {{{\mu _0}} \over {2\pi d}}\left( {{I_1} + {I_2}} \right)

240

MediumJEE Mains2006

In a region, steady and uniform electric and magnetic fields are present. These two fields are parallel to each other. A charged particle is released from rest in this region. The path of the particle will be a

Options:

A) helix

B) straight line

C) ellipse

D) circle

241

MediumJEE Mains2006

A long solenoid has $200 turns per cm and carries a current i. The magnetic field at its center is 6.28 \times {10^{ - 2}}\,\,\,Weber/{m^2}. Another long solenoid has 100 turns per cm and it carries a current {i \over 3}$. The value of the magnetic field at its center is

Options:

A) 1.05 \times {10^{ - 2}}\,\,Weber/{m^2}

B) 1.05 \times {10^{ - 5}}\,\,Weber/{m^2}

C) 1.05 \times {10^{ - 3}}\,\,Weber/{m^2}

D) 1.05 \times {10^{ - 4}}\,\,Weber/{m^2}

242

MediumJEE Mains2005

Two thin, long, parallel wires, separated by a distance $'d' carry a current of 'i' A$ in the same direction. They will

Options:

A) repel each other with a force of ${\mu _0}{i^2}/\left( {2\pi d} \right)

B) attract each other with a force of ${\mu _0}{i^2}/\left( {2\pi d} \right)

C) repel each other with a force $_0{i^2}/\left( {2\pi {d^2}} \right)

D) attract each other with a force of ${\mu _0}{i^2}/\left( {2\pi {d^2}} \right)

243

MediumJEE Mains2005

A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an electron is projected along the direction of the fields with a certain velocity then

Options:

A) its velocity will increase

B) Its velocity will decrease

C) it will turn towards left of a direction of motion

D) it will turn towards right of direction of motion

244

MediumJEE Mains2005

A charged particle of mass $m and charge q travels on a circular path of radius r that is perpendicular to a magnetic field B.$ The time taken by the particle to complete one revolution is

Options:

A) {{2\pi {q^2}B} \over m}

B) {{2\pi mq} \over B}

C) {{2\pi m} \over {qB}}

D) {{2\pi qB} \over m}

245

MediumJEE Mains2005

Two concentric coils each of radius equal to $2 \pi cm are placed at right angles to each other. 3 ampere and 4 ampere are the currents flowing in each coil respectively . The magnetic induction in Weber / {m^2} at the center of the coils will be \left( {\mu = 4\pi \times {{10}^{ - 7}}Wb/A.m} \right)

Options:

A) {10^{ - 5}}

B) 12 \times {10^{ - 5}}

C) 7 \times {10^{ - 5}}

D) 5 \times {10^{ - 5}}

246

MediumJEE Mains2004

A current $i$ ampere flows along an infinitely long straight thin walled tube, then the magnetic induction at any point inside the tube is

Options:

A) {{{\mu _0}} \over {4\pi }},{{2i} \over r}$ tesla

B) zero

C) infinite

D) {{2i} \over r}$ tesla

247

MediumJEE Mains2004

A long wire carries a steady current. It is bent into a circle of one turn and the magnetic field at the centre of the coil is $B. It is then bent into a circular loop of n$ turns. The magnetic field at the center of the coil will be

Options:

A) 2n B

B) {n^2}\,B

C) nB

D) 2{n^2}\,B

248

MediumJEE Mains2004

The magnetic field due to a current carrying circular loop of radius $3 cm at a point on the axis at a distance of 4 cm from the centre is 54\,\mu T.$ What will be its value at the center of loop?

Options:

A) 125\,\mu T

B) 150\,\mu T

C) 250\,\mu T

D) 75\,\mu T

249

MediumJEE Mains2004

Two long conductors, separated by a distance $d carry current {I_1} and {I_2} in the same direction. They exert a force F on each other. Now the current in one of them is increased to two times and its direction is reversed. The distance is also increased to 3d$. The new value of the force between them is

Options:

A) - {{2F} \over 3}

B) {F \over 3}

C) -2F

D) - {F \over 3}

250

MediumJEE Mains2003

A particle of mass $M and charge Q moving with velocity \overrightarrow v describe a circular path of radius R when subjected to a uniform transverse magnetic field of induction B.$ The network done by the field when the particle completes one full circle is

Options:

A) \left( {{{M{v^2}} \over R}} \right)2\pi R

B) zero

C) B\,\,Q\,2\pi R

D) B\,Qv\,2\pi R

251

MediumJEE Mains2003

A particle of charge $ - 16 \times {10^{ - 18}} coulomb moving with velocity 10m{s^{ - 1}} along the x-axis enters a region where a magnetic field of induction B is along the y-axis, and an electric field of magnitude {10^4}V/m is along the negative z-axis. If the charged particle continues moving along the x-axis, the magnitude of B$ is

Options:

A) {10^3}Wb/{m^2}

B) {10^5}Wb/{m^2}

C) {10^{16}}Wb/{m^2}

D) {10^{ - 3}}Wb/{m^2}

252

MediumJEE Mains2002

If a current is passed through a spring then the spring will

Options:

A) expand

B) compress

C) remains same

D) none of these

253

MediumJEE Mains2002

If in a circular coil $A of radius R, current I is flowing and in another coil B of radius 2R a current 2I is flowing, then the ratio of the magnetic fields {B_A} and {B_B}$, produced by them will be

Options:

A) 1

B) 2

C) 1/2

D) 4

254

MediumJEE Mains2002

If an electron and a proton having same momentum enter perpendicular to a magnetic field, then

Options:

A) curved path of electron and proton will be same (ignoring the sense of revolution)

B) they will move undeflected

C) curved path of electron is more curved than that of the proton

D) path of proton is more curved.

255

MediumJEE Mains2002

The time period of a charged particle undergoing a circular motion in a uniform magnetic field is independent of its

Options:

A) speed

B) mass

C) charge

D) magnetic induction

256

MediumJEE Mains2002

Wires $1 and 2 carrying currents i{}_1 and i{}_2 respectively are inclined at an angle \theta to each other. What is the force on a small element dl of wire 2 at a distance of r from wire 1 (as shown in figure) due to the magnetic field of wire 1$?

Options:

A) {{{\mu _0}} \over {2\pi r}}{i_1}{i_2}\,dl\,\tan \,\theta

B) {{{\mu _0}} \over {2\pi r}}{i_1}{i_2}\,dl\,\sin \,\theta

C) {{{\mu _0}} \over {2\pi r}}{i_1}{i_2}\,dl\,\cos \,\theta

D) {{{\mu _0}} \over {4\pi r}}{i_1}{i_2}\,dl\,\sin \,\theta

257

EasyJEE Mains2025

If an optical medium possesses a relative permeability of \frac{10}{\pi} and relative permittivity of \frac{1}{0.0885}, then the velocity of light is greater in vacuum than that in this medium by _________ times. $\left(\mu_0=4 \pi \times 10^{-7} \mathrm{H} / \mathrm{m}, \epsilon_0=8.85 \times 10^{-12} \mathrm{~F} / \mathrm{m}, \mathrm{c}=3 \times 10^8 \mathrm{~m} / \mathrm{s}\right)

Options:

258

MediumJEE Mains2025

A loop ABCDA , carrying current \mathrm{I}=12 \mathrm{~A}, is placed in a plane, consists of two semi-circular segments of radius R_1=6 \pi \mathrm{~m} and \mathrm{R}_2=4 \pi \mathrm{~m}. The magnitude of the resultant magnetic field at center O is \mathrm{k} \times 10^{-7} \mathrm{~T}. The value of k is_________.( Given \mu_0=4 \pi \times 10^{-7} \mathrm{Tm} \mathrm{A}^{-1} )

Options:

259

EasyJEE Mains2025

A 4.0 cm long straight wire carrying a current of 8 A is placed perpendicular to a uniform magnetic field of strength 0.15 T . The magnetic force on the wire is ________mN .

Options:

260

EasyJEE Mains2025

The magnetic field inside a 200 turns solenoid of radius 10 cm is 2.9 \times 10^{-4} ~\mathrm{Tesla}. If the solenoid carries a current of 0.29 A , then the length of the solenoid is _______ \pi \mathrm{cm}.

Options:

261

MediumJEE Mains2025

A tightly wound long solenoid carries a current of 1.5 A . An electron is executing uniform circular motion inside the solenoid with a time period of 75 ns . The number of turns per metre in the solenoid is _________. [Take mass of electron \mathrm{m}_{\mathrm{e}}=9 \times 10^{-31} \mathrm{~kg}, charge of electron \left|\mathrm{q}_{\mathrm{e}}\right|=1.6 \times 10^{-19} \mathrm{C}, $ \left.\mu_0=4 \pi \times 10^{-7} \frac{\mathrm{~N}}{\mathrm{~A}^2}, 1 \mathrm{~ns}=10^{-9} \mathrm{~s}\right]

Options:

262

MediumJEE Mains2025

A current of 5 A exists in a square loop of side \frac{1}{\sqrt{2}} \mathrm{~m}. Then the magnitude of the magnetic field B at the centre of the square loop will be p \times 10^{-6} \mathrm{~T}. where, value of p is ________ \left[\right. Take \mu_0=4 \pi \times 10^{-7} \mathrm{~T} \mathrm{~mA}^{-1} ].

Options:

263

EasyJEE Mains2025

A proton is moving undeflected in a region of crossed electric and magnetic fields at a constant speed of 2 \times 10^5 \mathrm{~ms}^{-1}. When the electric field is switched off, the proton moves along a circular path of radius 2 cm . The magnitude of electric field is x \times 10^4 \mathrm{~N} / \mathrm{C}. The value of x is _________. Take the mass of the proton =1.6 \times 10^{-27} \mathrm{~kg}.

Options:

264

EasyJEE Mains2025

Two long parallel wires X and Y, separated by a distance of 6 cm , carry currents of 5 A and 4A, respectively, in opposite directions as shown in the figure. Magnitude of the resultant magnetic field at point P at a distance of 4 cm from wire Y is x \times 10^{-5} \mathrm{~T}. The value of x is _________ . Take permeability of free space as \mu_0=4 \pi \times 10^{-7} SI units.

Options:

265

MediumJEE Mains2024

A straight magnetic strip has a magnetic moment of $44 \mathrm{~Am}^2. If the strip is bent in a semicircular shape, its magnetic moment will be ________ \mathrm{Am}^2. (given \pi=\frac{22}{7}$)

Options:

266

MediumJEE Mains2024

A square loop of edge length $2 \mathrm{~m} carrying current of 2 \mathrm{~A} is placed with its edges parallel to the x-y axis. A magnetic field is passing through the x-y plane and expressed as \vec{B}=B_0(1+4 x) \hat{k}, where B_o=5 T. The net magnetic force experienced by the loop is _________ \mathrm{N}$.

Options:

267

MediumJEE Mains2024

A square loop PQRS having 10 turns, area $3.6 \times 10^{-3} \mathrm{~m}^2 and resistance 100 \Omega is slowly and uniformly being pulled out of a uniform magnetic field of magnitude \mathrm{B}=0.5 \mathrm{~T} as shown. Work done in pulling the loop out of the field in 1.0 \mathrm{~s} is _________ \times 10^{-6} \mathrm{~J}$.

Options:

268

EasyJEE Mains2024

An electron with kinetic energy $5 \mathrm{~eV} enters a region of uniform magnetic field of 3 \mu \mathrm{T} perpendicular to its direction. An electric field \mathrm{E} is applied perpendicular to the direction of velocity and magnetic field. The value of E, so that electron moves along the same path, is __________ \mathrm{NC}^{-1}. (Given, mass of electron =9 \times 10^{-31} \mathrm{~kg}, electric charge =1.6 \times 10^{-19} \mathrm{C}$)

Options:

269

EasyJEE Mains2024

A coil having 100 turns, area of $5 \times 10^{-3} \mathrm{~m}^2, carrying current of 1 \mathrm{~mA} is placed in uniform magnetic field of 0.20 \mathrm{~T} such a way that plane of coil is perpendicular to the magnetic field. The work done in turning the coil through 90^{\circ} is _________ \mu \mathrm{J}$.

Options:

270

EasyJEE Mains2024

A circular coil having 200 turns, $2.5 \times 10^{-4} \mathrm{~m}^2 area and carrying 100 \mu \mathrm{A} current is placed in a uniform magnetic field of 1 \mathrm{~T}. Initially the magnetic dipole moment (\vec{M}) was directed along \vec{B}. Amount of work, required to rotate the coil through 90^{\circ} from its initial orientation such that \vec{M} becomes perpendicular to \vec{B}, is ________ \mu$J.

Options:

271

EasyJEE Mains2024

A solenoid of length $0.5 \mathrm{~m} has a radius of 1 \mathrm{~cm} and is made up of '\mathrm{m}' number of turns. It carries a current of 5 \mathrm{~A}. If the magnitude of the magnetic field inside the solenoid is 6.28 \times 10^{-3} \mathrm{~T} then the value of \mathrm{m}$ is __________.

Options:

272

MediumJEE Mains2024

A 2A current carrying straight metal wire of resistance $1 \Omega, resistivity 2 \times 10^{-6} \Omega \mathrm{m}, area of cross-section 10 \mathrm{~mm}^2 and mass 500 \mathrm{~g} is suspended horizontally in mid air by applying a uniform magnetic field \vec{B}. The magnitude of B is ________ \times 10^{-1} \mathrm{~T} (given, \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$).

Options:

273

MediumJEE Mains2024

Two parallel long current carrying wire separated by a distance $2 r are shown in the figure. The ratio of magnetic field at A to the magnetic field produced at C is \frac{x}{7}. The value of x$ is __________.

Options:

274

EasyJEE Mains2024

A rod of length $60 \mathrm{~cm} rotates with a uniform angular velocity 20 \mathrm{~rad} \mathrm{s}^{-1} about its perpendicular bisector, in a uniform magnetic filed 0.5 T$. The direction of magnetic field is parallel to the axis of rotation. The potential difference between the two ends of the rod is _________ V.

Options:

275

MediumJEE Mains2024

The magnetic field existing in a region is given by $\vec{B}=0.2(1+2 x) \hat{k}. A square loop of edge 50 \mathrm{~cm} carrying 0.5 A current is placed in x-y plane with its edges parallel to the x-y axes, as shown in figure. The magnitude of the net magnetic force experienced by the loop is _________ \mathrm{mN}$.

Options:

276

EasyJEE Mains2024

A moving coil galvanometer has 100 turns and each turn has an area of 2.0 \mathrm{~cm}^2. The magnetic field produced by the magnet is 0.01 \mathrm{~T} and the deflection in the coil is 0.05 radian when a current of 10 \mathrm{~mA} is passed through it. The torsional constant of the suspension wire is x \times 10^{-5} \mathrm{~N}-\mathrm{m} / \mathrm{rad}. The value of x is _______ .

Options:

277

MediumJEE Mains2024

A regular polygon of 6 sides is formed by bending a wire of length 4 \pi meter. If an electric current of 4 \pi \sqrt{3} A is flowing through the sides of the polygon, the magnetic field at the centre of the polygon would be x \times 10^{-7} \mathrm{~T}. The value of x is _________.

Options:

278

MediumJEE Mains2024

Two circular coils $P and Q of 100 turns each have same radius of \pi \mathrm{~cm}. The currents in P and R are 1 A and 2 A respectively. P and Q are placed with their planes mutually perpendicular with their centers coincide. The resultant magnetic field induction at the center of the coils is \sqrt{x} ~m T, where x= __________. [Use \mu_0=4 \pi \times 10^{-7} \mathrm{~TmA}^{-1}$]

Options:

279

EasyJEE Mains2024

An electron moves through a uniform magnetic field $\vec{B}=B_0 \hat{i}+2 B_0 \hat{j} T. At a particular instant of time, the velocity of electron is \vec{u}=3 \hat{i}+5 \hat{j} \mathrm{~m} / \mathrm{s}. If the magnetic force acting on electron is \vec{F}=5 e \hat{k} N, where e is the charge of electron, then the value of B_0 is _________ T$.

Options:

280

MediumJEE Mains2024

The current of $5 \mathrm{~A} flows in a square loop of sides 1 \mathrm{~m} is placed in air. The magnetic field at the centre of the loop is X \sqrt{2} \times 10^{-7} T. The value of X$ is _________.

Options:

281

EasyJEE Mains2024

A charge of $4.0 \mu \mathrm{C} is moving with a velocity of 4.0 \times 10^6 \mathrm{~ms}^{-1} along the positive y axis under a magnetic field \vec{B} of strength (2 \hat{k}) \mathrm{T}. The force acting on the charge is x \hat{i} N. The value of x$ is __________.

Options:

282

MediumJEE Mains2024

The magnetic field at the centre of a wire loop formed by two semicircular wires of radii $R_1=2 \pi \mathrm{m} and R_2=4 \pi \mathrm{m}, carrying current \mathrm{I}=4 \mathrm{~A} as per figure given below is \alpha \times 10^{-7} \mathrm{~T}. The value of \alpha is ________. (Centre \mathrm{O}$ is common for all segments)

Options:

283

EasyJEE Mains2024

Two long, straight wires carry equal currents in opposite directions as shown in figure. The separation between the wires is $5.0 \mathrm{~cm}. The magnitude of the magnetic field at a point \mathrm{P} midway between the wires is _______ \mu \mathrm{T} (Given : \mu_0=4 \pi \times 10^{-7} \mathrm{TmA}^{-1}$)

Options:

284

MediumJEE Mains2023

An electron in a hydrogen atom revolves around its nucleus with a speed of 6.76 \times 10^6 \mathrm{~ms}^{-1} in an orbit of radius 0.52 \mathrm{~A}^{\circ}. The magnetic field produced at the nucleus of the hydrogen atom is _________ T.

Options:

285

EasyJEE Mains2023

A straight wire $\mathrm{AB} of mass 40 \mathrm{~g} and length 50 \mathrm{~cm} is suspended by a pair of flexible leads in uniform magnetic field of magnitude 0.40 \mathrm{~T} as shown in the figure. The magnitude of the current required in the wire to remove the tension in the supporting leads is ___________ A. \left(\right. Take g=10 \mathrm{~ms}^{-2}$ ).

Options:

286

EasyJEE Mains2023

A straight wire carrying a current of $14 \mathrm{~A} is bent into a semi-circular arc of radius 2.2 \mathrm{~cm} as shown in the figure. The magnetic field produced by the current at the centre (\mathrm{O}) of the arc. is ____________ \times ~10^{-4} \mathrm{~T}

Options:

287

MediumJEE Mains2023

The ratio of magnetic field at the centre of a current carrying coil of radius $r to the magnetic field at distance r from the centre of coil on its axis is \sqrt{x}: 1. The value of x$ is __________

Options:

288

MediumJEE Mains2023

A proton with a kinetic energy of $2.0 ~\mathrm{eV} moves into a region of uniform magnetic field of magnitude \frac{\pi}{2} \times 10^{-3} \mathrm{~T}. The angle between the direction of magnetic field and velocity of proton is 60^{\circ}. The pitch of the helical path taken by the proton is __________ \mathrm{cm}. (Take, mass of proton =1.6 \times 10^{-27} \mathrm{~kg} and Charge on proton =1.6 \times 10^{-19} \mathrm{C}$ ).

Options:

289

EasyJEE Mains2023

Two identical circular wires of radius $20 \mathrm{~cm} and carrying current \sqrt{2} \mathrm{~A} are placed in perpendicular planes as shown in figure. The net magnetic field at the centre of the circular wires is __________ \times 10^{-8} \mathrm{~T}. (Take \pi=3.14$)

Options:

290

MediumJEE Mains2023

A charge particle of $2 ~\mu \mathrm{C} accelerated by a potential difference of 100 \mathrm{~V} enters a region of uniform magnetic field of magnitude 4 ~\mathrm{mT} at right angle to the direction of field. The charge particle completes semicircle of radius 3 \mathrm{~cm} inside magnetic field. The mass of the charge particle is __________ \times 10^{-18} \mathrm{~kg}

Options:

291

MediumJEE Mains2023

Two long parallel wires carrying currents 8A and 15A in opposite directions are placed at a distance of 7 cm from each other. A point P is at equidistant from both the wires such that the lines joining the point P to the wires are perpendicular to each other. The magnitude of magnetic field at P is _____________ $\times~10^{-6} T. (Given : \sqrt2=1.4$)

Options:

292

MediumJEE Mains2023

A single turn current loop in the shape of a right angle triangle with sides 5 cm, 12 cm, 13 cm is carrying a current of 2 A. The loop is in a uniform magnetic field of magnitude 0.75 T whose direction is parallel to the current in the 13 cm side of the loop. The magnitude of the magnetic force on the 5 cm side will be $\frac{x}{130} N. The value of x$ is ____________.

Options:

293

EasyJEE Mains2022

A closely wounded circular coil of radius 5 cm produces a magnetic field of $37.68 \times 10^{-4} \mathrm{~T} at its center. The current through the coil is _________A. [Given, number of turns in the coil is 100 and \pi=3.14$]

Options:

294

EasyJEE Mains2022

A wire of length $314 \mathrm{~cm} carrying current of 14 \mathrm{~A} is bent to form a circle. The magnetic moment of the coil is ________ A -\mathrm{m}^{2}. [Given \pi=3.14$]

Options:

295

MediumJEE Mains2022

A singly ionized magnesium atom (A = 24) ion is accelerated to kinetic energy 5 keV, and is projected perpendicularly into a magnetic field B of the magnitude 0.5 T. The radius of path formed will be _____________ cm.

Options:

296

MediumJEE Mains2022

A deuteron and a proton moving with equal kinetic energy enter into a uniform magnetic field at right angle to the field. If rd and rp are the radii of their circular paths respectively, then the ratio ${{{r_d}} \over {{r_p}}} will be \sqrt{x}$ : 1 where x is __________.

Options:

297

EasyJEE Mains2022

Two 10 cm long, straight wires, each carrying a current of 5A are kept parallel to each other. If each wire experienced a force of 10$-$5 N, then separation between the wires is ____________ cm.

Options:

298

EasyJEE Mains2021

A long solenoid with 1000 turns/m has a core material with relative permeability 500 and volume 103 cm3. If the core material is replaced by another material having relative permeability of 750 with same volume maintaining same current of 0.75 A in the solenoid, the fractional change in the magnetic moment of the core would be approximately $\left( {{x \over {499}}} \right)$. Find the value of x.

Options:

299

MediumJEE Mains2021

A uniform conducting wire of length is 24a, and resistance R is wound up as a current carrying coil in the shape of an equilateral triangle of side 'a' and then in the form of a square of side 'a'. The coil is connected to a voltage source V0. The ratio of magnetic moment of the coils in case of equilateral triangle to that for square is 1 : $\sqrt y $ where y is ................. .

Options:

300

MediumJEE Mains2021

A coil in the shape of an equilateral triangle of side 10 cm lies in a vertical plane between the pole pieces of permanent magnet producing a horizontal magnetic field 20 mT. The torque acting on the coil when a current of 0.2 A is passed through it and its plane becomes parallel to the magnetic field will be $\sqrt x \times 10-$5 Nm. The value of x is .................

Options:

301

EasyJEE Mains2021

Two short magnetic dipoles m1 and m2 each having magnetic moment of 1 Am2 are placed at point O and P respectively. The distance between OP is 1 meter. The torque experienced by the magnetic dipole m2 due to the presence of m1 is ........... $\times 10-$7 Nm.

Options:

302

MediumJEE Mains2020

A galvanometer coil has 500 turns and each turn has an average area of 3 $ \times $ 10–4 m2 . If a torque of 1.5 Nm is required to keep this coil parallel to a magnetic field when a current of 0.5 A is flowing through it, the strength of the field (in T) is ______.

Options:

302

Total Questions

Easy

202

Medium

Hard

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