  The magnetic field of moving vortices in anisotropic superconductors is
considered in the framework of time-dependent London approach. It is found that
at distances large relative to the core size, the field may change sign that
alludes to a non-trivial intervortex interaction which depends on the crystal
anisotropy and on the speed and direction of motion. These effects are caused
to the electric fields and corresponding normal currents which appear due to
the moving vortex magnetic structure. We find that the motion related part of
the magnetic field attenuates at large distances as $1/r^3$ unlike the
exponential decay of the static vortex field. The electric field induced by the
vortex motion decreases as $1/r^2$.
