This question is about Electromagnetic field without reference to electromagnetic waves I have the understanding that the electric field is not itself a wave.  And the magnetic field itself is not a wave.  If they were I assume somewhere someone would have said the terms electric wave or magnetic wave. At least I have not read it anywhere.
However I have noticed one thing very peculiar as I would put it, I have never yet seen anywhere that when it comes to an electromagnetic field, the subject immediately becomes electromagnetic waves and frequency and everything electromagnetic waves.  And out goes electromagnetic field and it immediately goes to the wayside. The waves just take over so to speak.
I do not want to know why this is.
I know where to find electric fields and magnetic fields.
What I like to know is where I can find Both fields together, i.e. electromagnetic field.  I know where I can find an electromagnetic field that is electromagnetic waves or becomes one or how to make electromagnetic fields propagate.
Some might say a static electromagnetic field as if it is a special type of it.  I only want to know the regular kind and not the one that takes off.
Thank you very much in advance.
 A: An electromagnetic wave is an electromagnetic field. Typically you can decompose electromagnetic fields into what is called the near field and what is called the far field. Waves traditionally refer to the far field, but both the near field and the far field are electromagnetic fields.
Any ordinary circuit, even a DC circuit, has a near field type electromagnetic field. In order to transfer energy, electromagnetism requires both an electric and a magnetic field. Neither transfers energy alone, according to Poynting’s theorem. The simple fact that a circuit transfers energy therefore indicates that it is an electromagnetic field, and the fact that the energy stays near the wires indicates that it is a near field.
A: *

*Fields and waves:

A field is a property that you can measure at any point in space and time.
A wave is a perturbation of a field that propagates in space and time.
An electromagnetic wave is a perturbation of the electromagnetic field that propagates in space and time.

*

*There are two theories that explain electromagnetic radiation:

One is a classical theory, the Maxwell's electromagnetic theory: electromagnetic waves are generated by charges or oscillating dipoles. The frequency of the waves depends on the oscillation frequency of the source.
The other one is a quantum theory, the Quantum Field Theory: in the quantum world, the radiation has a wave-particle nature. This radiation is emitted by transitions between different energy states of the particles that make up the matter. The frequency is proportional to de difference of the energy between the level involved.
According to Maxwell's electromagnetic theory the electromagnetic field is made up of the electric and magnetic field obeying the Maxwell equations. You can find all the information about how to get the Maxwell equations in the R. Wangsness - Electromagnetic fields (https://www.wiley.com/en-us/Electromagnetic+Fields%2C+2nd+Edition-p-9780471811862)
A: In electrostatics, a charge simply has a field given by the familiar equation $F = {kq \over d^2}$. There are no waves.
To generate waves, you jiggle the charge. That's what an antenna does. The wave sustains itself because Maxwell's equations say that a changing $E$ field produces a changing $B$ field which again produces a changing $E$ field...
The situation is the same with gravity waves. Gravity waves are produced when massive objects jiggle.
See the animation here. Notice that the field is disturbed when the charge accelerates from rest to a constant velocity.

http://www.tapir.caltech.edu/~teviet/Waves/empulse.html
A: Any circuit with transformers and capacitors, like a power supply unit for a computer for example, has a variable electromagnetic field inside.
EM waves are also EM fields. Both examples have in common that for each point of space and instant of time there is a defined value for the E and B field.
It is similar to other types of fields. There is  a variable elastic field in the suspension system of a car. A seismic wave is also an variable elastic field.
