We know that stationary charge produce electric field. Charges in uniform motion produce both electric and magnetic field. ACCELERATED CHARGE RADIATE ELECTROMAGNETIC WAVES. It is an important result of Maxwell's theory. Thus an electron produces all three electric field,magnetic field and electromagnetic waves.
Maxwell theory :
When electromagnetic waves propagate in space than electric and magnetic field oscillate in mutual perpendicular direction.
We know that time varying magnetic field produces electric field.
Maxwell explained that time varying electric field also produces magnetic field Maxwell formulated a set of equations (Maxwell questions) involving electric and magnetic field.
Maxwell formed the relation of time varying electric and magnetic field.
So combination of ampere law
Time dependent electric field and magnetic field give rise to each other.