I have a bit of trouble with understanding how electromagnetic fields. More specifically, how the magnetic and the electric component of the field interact. I am aware that a time-varying electric field will generate a magnetic field and vice versa. What I am having trouble understanding is how it manages to do so. How does a moving electric field suddenly become a magnetic field? I've tried to work it out from the equations but I'm having trouble understanding them. If anyone can point me in the right direction it would be greatly appreciated.