# Electromagnetic Radiation Emitted By An Accelerating Charge

## Main Question or Discussion Point

Suppose a point charge is slowly oscillating simple harmonically. Does it emit an electromagnet wave and if not why not ? How does its field change with time. Does anyone know of a good animation ?

Thanks.

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sophiecentaur
Gold Member
Hi and welcome to PF.
However "s..l..o..w..l..y" the charge oscillates, it will radiate a very low frequency wave.
There is a practical limit to what can actually be measured, however. The Energy of the oscillation gets lower as the frequency is reduced so, in the end, you just can't detect it; it will be below the noise level in any experiment.

Dale
Mentor
How does its field change with time.
The field from an arbitrarily moving point charge is given by the Lienard Wiechert potentials.

Thank you both. My intuition was confirmed.
So, this has nothing to do with 'near' and 'far' fields. I have not yet seen a clear, explanation of these terms and their significance. Would anyone like to try? Responses much appreciated.

Dale
Mentor
I have not yet seen a clear, explanation of these terms and their significance. Would anyone like to try
If you look at the Lienard Wiechert formulas (the fields, not the potentials) you will see that there are a couple of terms one term is proportional to $r^{-1}$ and one proportional to $r^{-2}$. The former is the far field and the latter is the near field. More generally, any field term that falls off faster than $r^{-1}$ is considered part of the near field.