  We study the space-average electromagnetic (EM) fields weighted by the energy
density in the central regions of heavy ion collisions. These average
quantities can serve as a barometer for the magnetic-field induced effects such
as the magnetic effect, the chiral separation effect and the chiral magnetic
wave. Comparing with the magnetic fields at the geometric center of the
collision, the space-average fields weighted by the energy density are smaller
in the early stage but damp slower in the later stage. The space average of
squared fields as well as the EM anomaly $\mathbf{E}\cdot\mathbf{B}$ weighted
by the energy density are also calculated. We give parameterized analytical
formula for these average quantities as functions of time by fitting numerical
results for collisions in the collision energy range $7.7-200$ GeV with
different impact parameters.
