When a charged particle at rest experiences zero 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 particle is at rest, its velocity $\vec{v} = 0$. The magnetic force component is $q(\vec{v} \times \vec{B}) = 0$, irrespective of the magnetic field $\vec{B}$.

The total force reduces to $\vec{F} = q\vec{E}$.

Given that the total electromagnetic force is zero, we have $q\vec{E} = 0$. Since the particle is charged ($q \neq 0$), the electric field $\vec{E}$ must be zero.

The magnetic field $\vec{B}$ does not exert any force on a particle at rest, so it might or might not be zero.