  The heavy-ion collisions can produce extremely strong transient magnetic and
electric fields. We study the azimuthal fluctuation of these fields and their
correlations with the also fluctuating matter geometry (characterized by the
participant plane harmonics) using event-by-event simulations. A sizable
suppression of the angular correlations between the magnetic field and the 2nd
and 4th harmonic participant planes is found in very central and very
peripheral collisions, while the magnitudes of these correlations peak around
impact parameter b~8-10 fm for RHIC collisions. This can lead to notable
impacts on a number of observables related to various magnetic field induced
effects, and our finding suggests that the optimal event class for measuring
them should be that corresponding to b~8-10 fm.
