# Electrics fields in Electromagnetic waves

It might sound naive but the question is:

In an Electromagnetic wave in a vacuum the electric and magnetic fields are vibrating but what are the source and drain of these fields?

An electric field must start from a charge and end or be in a circular fashion due to varying magnetic field and in a similarly way, magnetic fields must form a closed loop.

if magnetic fields are to be in closed loop always then the oscillating fields of a em waves must be too.

So what is the shape of fields in general near a em wave?

• Picture instead the electromagnetic waves as an electric potential in space rather than a physical vibrating wave Jan 23, 2020 at 11:13
• In general the shape is extremely varied. Perhaps the best place to start it to look at plane-wave solutions to Maxwell's Equations en.wikipedia.org/wiki/…, but there are many other solutions as well.
– Cryo
Jan 23, 2020 at 12:18
• Also note that in plane-wave there are no field loops, the field polarizations are uniform (with changing sign)
– Cryo
Jan 23, 2020 at 12:19

An EM wave in a vacuum is an ideal. Such a wave has an infinite extent in space and, by definition, there are no source charges and currents and so no field lines begin or end.

This works because even without charges or currents, a changing magnetic field acts as a source of electric field and vice-versa. The two fields co-exist and are manifestations of one electromagnetic field. In vacuum, Maxwell's equations are symmetric with respect to electric and magnetic fields.

Once you introduce sources or investigate how oscillating charges and currents produce electromagnetic waves, then those waves are not plane electromagnetic waves and only approximate to them; for the reasons that you put in your question.

It is simply not true that magnetic field lines must always form closed loops. The physical law is not "magnetic field lines must form closed loops", it's Maxwell's equations, of which the relevant one for this statement is $$\nabla \cdot B = 0$$, or "the divergence of the magnetic field vanishes everywhere".

As pointed out in the answers to this related question, vanishing divergence does not necessarily imply "closed field lines". It implies field lines that don't have a source or sink, i.e. lines that do not start or end at any particular point. There are two ways to satisfy this requirement: First, to have the field lines be closed loops, and second, to have the field lines be infinite straight lines without start or end.

The ideal case of the infinite plane electromagnetic wave falls into the second case, not the first.

An electric field must start from a charge and end or be in a circular fashion due to varying magnetic field and in a similarly way, magnetic fields must form a closed loop.

That affirmation are based on experimental facts about forces on charges, conducting wires and magnets. That forces are mathematically described by means of electric and magnetic fields. Anyway EM waves don't violate Maxwell equations, but comes from them if charges and currents are zero.

But it is also a fact that a charge alone, far from any other charge or current can have accelerated movement instead of being at rest. That movement is mathematically described by means of the notion of an EM wave.

I think it is basically an experimental fact. When Maxwell derived EM waves from its equations, they were supposed to propagated in a type of mechanical medium.

That they were later shown to propagate without any medium was not in the initial "design".