# How do we go from having electric and magnetic fields to an electromagnetic wave?

I'm trying to understand how electromagnetic radiation is created and can propagate through the void. I do understand the concept of an electromagnetic field. But I don't understand how we get from a "field" to a "wave".

I'm not really interested in detailed mathematics of how this happens, rather I'm looking for a complete high-level answer that to the extent possible:

• Explains every step of how we get from having nothing to having an electromagnetic wave that propagates through space (e.g wifi signal) and
• Provides clear and intuitive justification for any point/law/fact it uses.

Preferably all of this should be included within the answer but I do appreciate inclusion of helpful links and references for additional context.

Below is my current understanding along with some more specific questions.

• You make some charge move (e.g through an antenna by creating an oscillating dipole).
• This moving charge creates fluctuating electric fields and magnetic fields around it
• All good so far as this is what you expect a charge to do, however these fields will become weaker proportional to inverse square of the distance and you would expect them to basically disappear at a distance.
• Electric and magnetic fields somewhat magically interact and now you have a self-perpetuating wave that doesn't fade out like the field.

I don't understand this part, e.g how we get from a "field" to a "wave" and unfortunately most of the resources I tend to skip over why. I believe there should be a better explanation.

For example, according to Wikipedia, Faraday/Len/Lorentz laws have to do with this. However all these laws/theories require a conductive "circuit" that we don't have in the air in the vacuum of space (I do understand how these laws explain how your antenna would receive an electromagnetic signal).

Considering magnetic and electric fields/forces will act on charged particles, this raises a few questions:

• Does the magnetic field produced by the antenna somehow create charge in the air surrounding it?
• If the whole wave propagation is based on interactions between the fields and charged particles, then how can a wave propagate through the void of space when there is no charge?

Thanks!

Your summary of how time-varying electromagnetic fields are generated from moving charges is the beginning. But then, in vacuum, the Ampere-Maxwell law says that a changing electric field is associated with a magnetic field. Meanwhile, Faraday's law says that a changing magnetic field is associated with an electric field.

Neither of these statements requires stationary or moving charges (aka currents) and charges and currents are not needed to allow an electromagnetic wave to propagate.

Note that the electric and magnetic field strengths from the example of an oscillating electric dipole vary with the inverse of distance from a source, not as the inverse squared distance.

• can you clarify the last statement about how field strength varies as inverse distance not inverse squared distance?Thanks Jun 23 at 0:55

The simplest starting point it Jefimenko's equations (https://en.wikipedia.org/wiki/Jefimenko%27s_equations), which are another form of Maxwell's Equations.

The point is that and point in space and time $$(\vec r, t)$$, the electric and magnetic fields are caused by the charges, currents and their time derivatives on the past light-cone. That's it.

If you consider your dipole antenna example, and put it though 1 oscillation, the point where that oscillation is on the past light cone will move spherically outward at $$c$$, and that will be the only non-zero fields present, and they will fall as $$1/r$$, so the power falls as $$1/r^2$$, and the total power integrate over the sphere remains constant.

So in this picture, there is no propagating wave, as the $$E$$ and $$B$$ fields are not caused by each other, rather causality is propagating at $$c$$, revealing the charges and currents to points further away.

This is a brief nonmathematical explanation based on a diagram in Purcell’s textbook. If you’re familiar with the electric field lines representation for electric field strength, you can imagine those lines emerging out of the point charge at a velocity of the speed of light. You might imagine this is something similar to spaghetti emerging from a pasta, extruder, or water out of a hose.

Kinks in those lines can be generated by vibrating the charge, in other words, causing the charge to accelerate. Because the lines are moving out of the charge, kind of like spaghetti out of a spaghetti yet extruder, the kink will propagate at the speed of light.

You can see a mechanical analogy of this by running water out of a hose, and then shaking the hose, you will see the wave pattern that is generated.

The magnetic field part of the wave can be justified from Maxwells equations, with the change in the electric field, causing a change in the magnetic field. And vice versa.

... I don't understand how we get from a "field" to a "wave".

I'm not really interested in detailed mathematics of how this happens, rather I'm looking for a complete high-level answer ...

High level answer: So I think this has to do with the relationship between a field, f, and a wave, w, propagating through it. Commonly they are related through the derivative D (time or space). Eg w = Df. If a change occurs in the source of the field the values of the field must change and those values are changed by the propagating wave, w in accordance with w = Df. f is the integral of w.

A simple intuitive example: Consider a lone charge, q. An E field will extend from it with its amplitude falling off as 1/r, E = q/r. If the lone charge instantly changes to two charges the E field will not instantly change. A wave will propagate outward (here it would be a monopolar pulse) at the propagation speed of the field's medium (eg c) where in front of the pulse E = q/r and behind the pulse E = 2q/r. So the wave communicates a change in the field's source to the field.