What is the connection between electromagnetic field and electromagnetic wave?

Answer 1

There is an important law in physics which says that a moving or changing electric current produces a magnetic field. This is the reason electromagnets and motors work. The opposite is also true. A moving or changing magnetic field produces an electric current. This is the way electric generators work. If we have a high frequency alternating current moving through a conductor, as this electric field continually rises and collapses (it's alternating, remember) it produces a magnetic field at right angles to it. As this magnetic field rises and collapses it produces another electric field which in turn produces a magnetic and so on. This is a self propogating process which once started will continue moving through space forever. At sufficiently high frequency this produces a wave motion called an electromagnetic field which travels away from the conductor in all directions in ever widening circles much like moving your hand rapidly in water causes widening waves to travel on the surface. Because they travel in widening circles these waves are referred to as radiation, from the word radius which means like the spokes of a wheel. Depending on their frequency (how many times the waves rise and fall per second) we can classify many types of electromagnetic radiation such as light, radio waves, microwaves, gamma radiation..... This is a highly simplified description of what really happens and it might not satisfy some scientific purists but it works with my students. Hope it helps you.

Answer 2

The electromagnetic waves are composing by electromagnetic fields, perpendicular between them and perpendiculars to the propagation velocity.

Or one electromagnetic wave is composing by an electric field and magnetic field oscillating.