Electric Field vs Electromagnetic Field

Islam Hassan

If we have a static electric charge, it generates an electric field. If that static electric charge is accelerating, it generates an electromagnetic field.

What about if the electric charge is moving with uniform velocity? Is the field thus generated an electic field or an electromagnetic field?

And what about the energy of the field? When an accelerating electric charge slows and moves at a uniform velocity, where does the energy of acceleration of the electromagnetic field go? Likewise when a moving electic charge comes to a stop, is there any field energy associated with the movement which is dissipated and where does it go?


IH

mfb

In frames where the electric charge is moving, the field has an electric and a magnetic component. At the same time, in frames where the charge is at rest, the field is just an electric field. Therefore, the answer depends on the reference frame.

There is no "energy of acceleration of the electromagnetic field". Every acceleration needs an external field and therefore an external energy source/drain, so it is tricky to consider energy conservation in an explicit way for those setups. There are general theorems which guarantee global energy conservation, however.

vanhees71

To amply the answer of the previous poster: From the modern point of view there is only one and only electromagnetic field. It's one entity and cannot be split in an electric and a magnetic part, because that's an observer-dependent splitting. This is nicely demonstrated by the example under discussion: If you have a uniformly moving charge in one reference frame, an observer in this frame would measure both an electric and a magnetic field (or better said electric and magnetic components of the electromagnetic field), while an observer moving in the rest frame of the charge measures only the electric components, while the magnetic components vanish.

Islam Hassan

Thank you for your clarification. Is this what we would expect to be case in reality or simply a convenient way of explaining things?

Also re the energy of an electromagnetic field, I take it this is not affected by an observer's reference frame but is a quality inherent to the field itself. Is this correct?


IH

vanhees71

I don't know what you mean by "reality" here. The electromagnetic field and its interaction with charged particles are best described by a relativistic field theory, known as electrodynamics or Maxwell's equations. In this sense the above picture is our best knowledge about the "reality" of fields.

Energy and momentum together build a four vector in Minkowski space. Energy and momentum are of course observer-dependent quantities as in non-relativistic physics too.