# Electromagnetic Radiation

This isn't really a homework question, but I felt it was better suited here than in General Physics. I'm looking for more of a general explanation than anything. I was able to do my homework for this section on my own (mostly), but I feel like I still really have no idea what is actually going on.

So. Electromagnetic radiation. I feel like I'm missing something important to understanding. Basically what I know is this: moving charges can radiate an electric field and a magnetic field. How do we know what direction the fields radiate in? And how do we know in which direction they point? And finally, how can the phenomena be explained?

I tried reading the textbook for answers to these questions, but my course's textbook is a very dry read and was hard to follow. I didn't get much out of it.

Thanks very much in advance for any help.

## Answers and Replies

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Mere motion does not produce radiation. Acceleration does.

Radiation emission is a vast subject, covering lasers, X-ray machines, and radio stations to name just three. It would help knowing what particular situation you had in mind.

Simon Bridge
Science Advisor
Homework Helper
How do we know what direction the fields radiate in? And how do we know in which direction they point?
We measure them.
Check the definition of the electric and magnetic field.

And finally, how can the phenomena be explained?
Are you happy with a stationary charge having an electric field?

If you suddenly shift the charge to another location[1], then the field strength through all space has to change.
But this cannot happen everywhere at once - since nothing travels faster than light.
So the change in the electric field must propagate outwards at some speed.

Note: this is somewhat simplistic - but it should give you the idea of how something can be propagating outwards from a charge that shifts it's position. Details can be filled in from there.

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[1] this requires an acceleration

WannabeNewton
Science Advisor
The direction of propagation of the radiation field at a given point in space at some instant of time is given by the Poynting vector ##\vec{S}## at that point where ##\vec{S} = \frac{c}{4\pi}\vec{E}\times \vec{B}## in Gaussian units. The profile of the radiation depends crucially on the system generating the radiation; one simple case is spherically symmetric radiation.

phyzguy
Science Advisor
The direction and magnitude of the electric and magnetic fields, and the direction of propagation of the EM radiation, depend on the velocity and acceleration of the moving charge. There is a formula, called the Larmor formula, that let's you calculate the fields and the amount of power radiated in all directions. It is derived from Maxwell's equations. This Wikipedia page has a basic description. The best reference for this is Jackson's "Classical Electrodynamics", which goes through this in detail.

I guess the explanation behind EM radiation is pretty straightforward. I may have overcomplicated it in my head earlier. But I'm still not 100% confident on the directions of the fields/their propagation.

For example, how dow we know that in this situation, they propagate in the positive y direction?

phyzguy
Science Advisor
If you look at the solution for source-free Maxwell's equations in free space, EM waves must have E perpendicular to B, propagating in a direction perpendicular to both E and B. Note that in the simple case of your animation, a charge in simple harmonic motion in the z-direction, they don't just propagate in the +y direction, they propagate out in all directions with an intensity proportional to (sin(theta))^2. So the intensity is maximum in the x-y plane, and drops off to zero in the +/- z-directions.

Simon Bridge
Science Advisor
Homework Helper
We know the directions of the E and B fields because we have measured them in controlled circumstances designed to show if the math is wrong.
I suspect the problem here is that, since you are just starting out, the examples you have are pretty simple and conceptual.

Sorry for not responding sooner - been extremely busy with school lately. One final question, I think I feel better about the rest of this so far.

If, in the example gif I posted earlier, the charge is accelerating parallel to the z axis, why isn't there a radiative field in the z-direction? It seems to me the electric field would be changing constantly at a fixed point on the z-axis. I suppose there would be no magnetic field because the motion of the particle would be parallel to the direction vector.

Simon Bridge
Science Advisor
Homework Helper
I suppose there would be no magnetic field because the motion of the particle would be parallel to the direction vector.
Well done.

The instantaneous change in the electric field does propagate outwards - it's a relativistic effect sustained by the changing position of the charge and the finite speed of light. Whether you see a magneic effect depends on your relative motion. Not part of the classical model.

I brought up the relativity part just to get you thinking - which seems to have worked :)
Classically, EM radiation is a solution to Maxwell's equations that is, kinda, self-sustaining. For that you need an electric field changing in such a way that the resulting magnetic field will, in turn, change in such a way as to produce the original changing electric field and so on. For a charge oscillating along the z-axis (which direction is defined by the charge oscillations btw), there is no EM radiation along the z axis because the needed conditions do not occur in that direction. As you have noticed: no B-field.

For details, unfortunately, you have to do the math.