# How do moving charges change the evolution of a magnetic field?

$\setminus \nabla \setminus \times B = \setminus {\mu}_{0} J + \setminus {\mu}_{0} \setminus {\epsilon}_{0} \frac{\setminus \partial E}{\setminus \partial t}$.
This equation says that the magnetic field is generated by a current $J$ or an electric field that changes in time $E$ (if the electric field is constant, its time derivative is zero).