  We present the spatial distributions of electromagnetic fields ($\bf E$ and
$\bf B$) and electromagnetic anomaly $ \bf E \cdot B$ in Au+Au collisions at
the RHIC energy $\sqrt{s}$=200 GeV based on a multi-phase transport model. A
dipolar distribution of $\bf E \cdot B$ is observed in non-central collisions.
We find that the coupling of the $\bf E \cdot B$ dipole and magnetic field $\bf
B$ can induce an electric quadrupole moment which can further lead to the
difference in elliptic flows between positive charged particles and negative
charged particles through final interactions. The centrality dependence of the
density of $\bf E \cdot B$ is similar to the trend of the slope parameter $r$
measured from the difference in elliptic flows between positive pions and
negative pions by the STAR collaboration. Therefore, the novel mechanism for
electric quadrupole moment generation can offer a new interpretation of the
observed charge-dependent elliptic flow of pions, but without the formation of
chiral magnetic wave.
