If a charged particle at rest experiences no electromagnetic forc… - Vidyadip

MCQ

If a charged particle at rest experiences no electromagnetic force:

A
The electric field must be zero.
B
The magnetic field must be zero.
C
The magnetic field may or may not be zero.
✓
A and C both

✓

Answer

Correct option: D.

A and C both

Explanation:
Force on charged particle in an electric eld, $F = qE \ldots (1)$
Force on charged particle in a magnetic eld $F = q ( v \times b )= qvB \sin \theta \ldots (2)$
Where boldface letter represent vector nature of that quantity, $q$ is charge of the particle, $v$ is the velocity of the particle( if any), and $\theta$ is the angle between velocity and magnetic eld.
From (1), $F _{ E }=0$ only when either $q =0$ or $E =0$.
Let $q \neq 0$, and $F \neq 0$, then we must have $E \neq 0$
From (2), if $q \neq 0, v \neq 0$ and $B \neq 0$ even then $F_B$ can be 'zero' because of $\theta=0^{\circ}$ or $180^{\circ}$

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