It takes time for electromagnetic fields to travel from their source. We can calculate how electromagnetic fields propagate from a current source by using the equations
I solved these equations analytically for a current source which increases linearly with time. We can see that the electromagnetic waves spread out at the speed of light, the electric field points outwards, and the magnetic field swirls around the current source.
I also solved these equations numerically for a the typical form of a current caused by induction effects. We can see that initially there is an electromagnetic field that travels outwards. But then the magnetic field stabilizes as the current stops changing.
Lastly, I solved these equations numerically for a sine current. We can see that electromagnetic waves are propagating outwards from the source.
