When a charged particle held at rest experiences an electromagnetic...

The electromagnetic force on a charged particle is given by the Lorentz force equation:

$\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$

Since the charged particle is at rest, its velocity $\vec{v} = 0$. Substituting this into the force equation gives:

$\vec{F} = q\vec{E}$

It is given that the particle experiences an electromagnetic force, so $\vec{F} \neq 0$. This implies that $q\vec{E} \neq 0$, and hence the electric field $\vec{E}$ cannot be zero.

The magnetic force term $q(\vec{v} \times \vec{B})$ is zero regardless of the value of the magnetic field $\vec{B}$ because $\vec{v} = 0$. Thus, the magnetic field might or might not be zero.