Question 36: EM waves

Question

$$ 	ext { Match List - I with List - II. } $$
List - I
Relation
List - II
Law
A.
$$
\oint \vec{E} \cdot \overrightarrow{d l}=-\frac{d}{d t} \oint \vec{B} \cdot \overrightarrow{d a}
$$
I.
Ampere's circuital law
B.
$$
\oint \vec{B} \cdot \overrightarrow{d l}=\mu_0\left(I+\epsilon_0 \frac{d \phi_E}{d t}ight)
$$
II.
Faraday's laws of electromagnetic induction
C.
$$
\oint \vec{E} \cdot \overrightarrow{d a}=\frac{1}{\epsilon_0} \int_{\mathrm{v}} ho \mathrm{dv}
$$
III.
Ampere - Maxwell law
D.
$$
\oint \vec{B} \cdot \overrightarrow{d l}=\mu_0 I
$$
IV.
Gauss's law of electrostatics
Choose the correct answer from the options given below :

Accepted Answer

For relation A
The equation $\oint \vec{E} \cdot d \vec{l}=-\frac{d}{d t}[\oint \vec{B} \cdot d \vec{a}]$ mathematically states that the line integral of the electric field around a closed loop is equal to the negative rate of change of magnetic flux through the loop. This is the integral form of Faraday's Law of Electromagnetic Induction, i.e., $\mathrm{A} ightarrow$ II
For relation B
This equation $\oint \overrightarrow{\mathrm{B}} \cdot \mathrm{d} \overrightarrow{\mathrm{l}}=\mu_0\left(\mathrm{I}+\epsilon_0 \frac{\mathrm{~d} \Phi_{\mathrm{E}}}{\mathrm{dt}}ight)$ relates the magnetic field line integral to both the conduction current (I) and the displacement current $\left(\epsilon_0 \frac{\mathrm{~d} \Phi_{\mathrm{E}}}{\mathrm{dt}}ight)$. This modification to Ampere's Law was introduced by Maxwell to account for changing electric fields. This is the Ampere-Maxwell Law, i.e., $\mathrm{B} ightarrow$ III
For relation C
In relation $C, \oint \vec{E} \cdot d \vec{a}=\frac{1}{\epsilon_0} \int_V ho d V$ the total charge $Q_{	ext {enclosed }}$ is represented as $\oint \vec{E} \cdot d \vec{a}$. The equation states that the total electric flux through a closed surface is equal to the enclosed charge divided by $\epsilon_0$. This is Gauss's Law of Electrostatics, i.e., $\mathrm{C} ightarrow$ IV
For relation D
This relation $\oint \overrightarrow{\mathrm{B}} \cdot d \overrightarrow{\mathrm{l}}=\mu_0 \mathrm{I}$ states that the line integral of the magnetic field around a closed loop is equal to $\mu_0$ times the current enclosed by the loop. This is the original form of Ampere's Circuital Law which is valid for steady currents, i.e., $\mathrm{D} ightarrow \mathrm{I}$
So, the correct match is $\mathrm{A} ightarrow$ II, $\mathrm{B} ightarrow$ III, $\mathrm{C} ightarrow$ IV, $\mathrm{D} ightarrow$ I. Hence, the correct option is (B).

Answer

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

Answer

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

Answer

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

Answer

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

EM waves

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