Question

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

Answer 1

The relationship between moving charges and magnetic field is regulated by the Ampère's law (that is one of the Maxwell equations).

`\nabla\times B=\mu_0J+\mu_0\epsilon_0(\partial E)/(\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).