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.
✓
The electric field may or may not be zero.
D
The magnetic field may or may not be zero.

✓

Answer

Correct option: C.

The electric field may or may not be zero.

Force on charged particle in an electric eld, $\text{F} = \text{qE} \ ...(1)$
Force on charged particle in a magnetic eld $\text{F} = \text{q} (\text{v}\times\text{b}) = \text{qvB} \sin\theta \ ...(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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