If a charged particle at rest experiences no electromagnetic force,

Explanation

Electric field can apply force on a charged particle in a state of rest or motion. If the charge particle is in a state of motion only then magnetic force can act on it. In a state of motion there is one possibility of cancellation of electric and magnetic force. Here, charge is in a state of rest and experiencing no electromagnetic force, hence, electric field must be zero in the surrounding. For magnetic field, we cannot say anything, because particle is at rest and magnetic force will remain sero even if magnetic field is present. So in the given situation, electric field must be zero but magnetic field may or may not be zero.