We show that fluctuating proton positions in the colliding nuclei generate, on the event-by-event basis, very strong magnetic and electric fields in the direction both parallel and perpendicular to the reaction plane. The magnitude of E and B fields in each event is of the order of Gauss. Implications on the observation of electric dipole in heavy ion collisions is discussed, and the possibility of measuring the electric conductivity of the hot medium is pointed out.