Question

How does an electric field creates a magnetic field?

Answer 1

Electrically charged particles act as a source of the electromagnetic field. If a charged particle popped into existence we could imagine tubes of electric flux (D) flowing outward at the speed of light. If we move the charge around, relative to some frame of reference, we find lines of some magnitude of magnetic field intensity (H) wrapping around the particle's line of motion. The force-defining electric field intensity (E) and induction field (B) can be derived using the constitutive relations for a vacuum.

The E and B fields are calculated using  Jefimenko's equations.

Answer 2

 When an electric charge moves, its field will change as a function of time. Consequently, there will be a magnetic field. This is known as Ampere's law: