An extraordinary strong electromagnetic field is expected to be generated in off-central relativistic heavy ion collisions, resulting in a splitting in the directed flow $v_1$ of charged particles with opposite charge or ($D^0,\overline{D}^0$) charmed mesons. Despite the complex dynamics of charged particles due to the strong interactions with QGP, it is possible at $p_T > m$ to directly correlate the splitting in the anisotropic flows $v_n$ of charged particles with opposite charge to some main features of the magnetic field. In particular for the slope of the splitting $d\Delta v_1/dy_z|_{y_z=0}$ of positively and negatively charged particles at high $p_T$, it can be formulated as $d\Delta v_1/dy_z|_{y_z=0}=-\alpha \frac{\partial \ln f}{\partial p_T}+\frac{2\alpha-\beta}{p_T}$, where $f$ is the $p_T$ spectra of the charged particles and the constants $\alpha$ and $\beta$ are constrained by the $y$ component of magnetic fields and the sign of $\alpha$ is simply determined by the difference $\Delta[tB_y(t)]$ in the center of colliding systems at the formation time of particles and at the time when particles escape e.m. fields or freeze out. It
supplies a useful guide to quantify the effect of different magnetic field configurations and provides an evidence
of why the measurement of $\Delta v_1$ of heavy quarks and leptons decayed from $Z^0$ boson and their correlations
are a powerful probe of the initial strong e.m. fields in relativistic collisions.