Question 38: Magnetism and Matter

Question

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 :

Accepted Answer

According to the Lorentz force law, the force experienced by a charged particle, such as an electron, moving in a magnetic field is given by the equation:
$ \overline{\mathrm{F}} = \mathrm{q}(\overline{\mathrm{v}} 	imes \overline{\mathrm{B}}) $
Here, $ \overline{\mathrm{F}} $ is the force exerted on the particle, $ \mathrm{q} $ is the charge of the particle, $ \overline{\mathrm{v}} $ is the velocity vector of the particle, and $ \overline{\mathrm{B}} $ is the magnetic field vector. The symbol $ 	imes $ indicates the cross product, meaning the force is perpendicular to both the velocity and magnetic field vectors.
Given this, for the force $ \overline{\mathrm{F}} $ to be zero:
The velocity $ \overline{\mathrm{v}} $ and the magnetic field $ \overline{\mathrm{B}} $ must be parallel (or anti-parallel). This condition will result in the angle $ 	heta = 0^\circ $ or $ 180^\circ $.
Under these circumstances, the electron will not experience any magnetic force and will continue to move in a straight line with constant velocity, as the cross product becomes zero. Therefore, the reason (R) is indeed a valid explanation: the magnetic field being along the direction of the electron's velocity means no perpendicular force is applied to change its path.

Answer

(A) is true but (R) is false

Answer

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

Answer

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

Answer

(A) is false but (R) is true

Magnetism and Matter

Choose the correct answer: