Question

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 electric field may or may not be zero
(d) the magnetic field may or may not be zero

Answer 1

(a) the electric field must be zero
(d) the magnetic field may or may not be zero

As the charged particle is at rest, its velocity, V = 0 and magnetic force, F = qVB = 0. Hence, we cannot determine whether a magnetic field is present or not.
But as the particle at rest experiences no electromagnetic force, the electric field must be zero. This is because electric force acts on a particle whether it is at rest or in motion.