  We consider crossed electric and a magnetic fields
$\left(\vec{B}=B\,\hat{z},~\vec{E}=E\,\hat{y}\right)$, with $E/B<1$, in
presence of some initial number of $e^{\pm}$ pairs. We do not discuss here the
mechanism of generation of these initial pairs. The electric field accelerates
the pairs to high-energies thereby radiating high-energy synchrotron photons.
These photons interact with the magnetic field via magnetic pair production
process (MPP), i.e. $\gamma+B\rightarrow e^{+}+e^{-}$, producing additional
pairs. We here show that the motion of all the pairs around the magnetic field
lines generates a current that induces a magnetic field that shields the
initial one. For instance, for an initial number of pairs $N_{\pm,0}=10^{10}$,
an initial magnetic field of $10^{12}$ G can be reduced of a few percent. The
screening occurs in the short timescales $10^{-21}\leq t \leq 10^{-15}$ s, i.e.
before the particle acceleration timescale equals the synchrotron cooling
timescale. The present simplified model indicates the physical conditions
leading to the screening of strong magnetic fields. To assess the occurrence of
this phenomenon in specific astrophysical sources, e.g. pulsars or gamma-ray
bursts, the model can be extended to evaluate different geometries of the
electric and magnetic fields, quantum effects in overcritical fields, and
specific mechanisms for the production, distribution, and multiplicity of the
$e^{-}e^{+}$ pairs.
