# About accelerating charges

1. May 8, 2013

### tmv3v

So we know that an accellerating charge will emit EM waves.

Consider putting a voltage through a circular wire. Electrons are travelling in the wire with constant speed but their velocity is changing constantly as it is changing direction due to the shape of the wire. Now does that mean the electron will emit EM waves?

Consider another scenario, we now have a charged metal sphere. Does it emit EM wave if we let it drop to the ground?

2. May 8, 2013

### Staff: Mentor

A ring with a constant current does not emit EM waves - the contributions from all electrons together cancel each other.
The gravitational acceleration triggered a lot of discussion, and as far as I know, there is no clear answer yet.

3. May 8, 2013

### tmv3v

how about a straight wire and you turn up the voltage making electrons accelerate?

4. May 9, 2013

### Staff: Mentor

You need some time-dependence in the current, otherwise it will not work.

5. May 9, 2013

### tmv3v

So as you increase voltage constantly,
your current increases comstantly, and therefore the electrons are accelerating in the wire with constant acceleration (dV/dt = c>0 dI/dt > 0 dv/dt = a >0). So what kind of EM wave do the electrons emit?

6. May 9, 2013

### Staff: Mentor

That should give some radiation. What do you mean with "what kind of EM wave"? The frequency will depend on the setup, and I doubt that it is possible to give an answer without a detailed analysis (and probably a numerical simulation).

7. May 9, 2013

### tmv3v

Oh because I can't image how radiation will be given off by a piece of wire. Say we increase the voltage from 1V to 12V in 12seconds, so that dV/dt = 1, and we connect a copper wire to the adjustable power source, where the copper wire has a radius of 5mm. What radiation will the electrons from the wire give off?

8. May 9, 2013

### Staff: Mentor

dV/dt = 1 [highlight]V/s[/highlight]
Actually, 11/12 and not 1.

It is impossible to answer this without knowledge of the cable shape, and probably numerical simulations (and nobody wants to do them unless it has some real application, I think). The circuit will emit a tiny amount of extremely-low-frequency radiation.

9. May 9, 2013

### tmv3v

So it actually emits radiation, and I think every electrical appliances we use will emit very low frequency radiation too? Also, how about if we accelerate a piece of wire horizontally (say we hold the wire and run across the room). Can we treat this as acceleration of a charge? If we can, and another person is observing this, will he see the radiation but I will not because I am in the same frame of reference as the wire?

10. May 9, 2013

### Staff: Mentor

Sure. The dominant contribution has the same frequency as the power grid, usually 50 or 60 Hz.
If the wire is charged or has charged parts, it will radiate a bit.

The existence of radiation is frame-independent. You are not in an inertial frame if you accelerate.

11. May 9, 2013

### DrewD

Is there a good place to read a detailed description of this? I assume it is a quantum effect. I tutor and teach at the lower undergraduate and High School level, and I have been asked this a couple of times about this which seems like a reasonable question to me (or maybe I'm just forgetting something obvious). Since I don't fully understand why this is the case, I didn't want to make up a misleading analogy.

12. May 9, 2013

### tmv3v

Mmm.. interesting! 50-60Hz is in the radio wave range so we should get a small interference when we turn on the radio with a lot of electrical appliances operating around us!

I am just wondering, what is the difference between putting an increasing current through a wire and accelerating the whole wire horizontally as when you consider electrons in the wire they are accelerating in space in both cases?

Good point about frame-independent:D Yeah I forgot that EM waves travel at the speed of light in all frame of reference!

13. May 9, 2013

### tmv3v

Yes I totally agree! Once you are taught about an accelerating charge will emit EM waves, you will recall what you have learnt, eg:

1) electrons in circuits (in fact positive holes in metals as well)
2) Electrons orbiting a positive nucleus (we know that they are not really orbiting and it is all about probability when you get into college physics/chemistry but there is still a chance for the electrons to accelerate)
3) In fact all matter contains electrons and protons, meaning everything emits EM waves then?

If it is true well we know that the radiation is very small that it is hard to have an effect. However in theory radiation should exist for any charged particles (as they all have some probability to accelerate).

14. May 9, 2013

### Staff: Mentor

A classical description works fine here.
Textbooks about electromagnetism should cover this in some way.

Radios operate in the range of several kHz to many MHz, some orders of magnitude above the frequency of the power grid.
Don't forget the protons, and the direction and magnitude of acceleration.

15. May 9, 2013

### cosmik debris

Do a search on "Do Uniformly Accelerated Charges Radiate?". You may be surprised at the different answers to this.

16. May 9, 2013

### WannabeNewton

If the issue is taking radiation due to uniform acceleration of a charge (assuming you can somehow maintain uniform acceleration by applying an external force, because the charge solely on its own will undergo back reaction from the radiation due to the Abraham-Lorentz self force and will cease to undergo uniform acceleration) and then applying the equivalence principle to get what is ostensibly a nonsensical answer, note that you cannot apply the equivalence principle in such a case because the mass-energy distribution is not localized (the electromagnetic field carried by the charge extends out to infinity).

17. May 9, 2013

### Jano L.

Actually, it is simple consequence of the Maxwell equations. If the currents are stationary (do not vary in time), there is no production of radiation from them.

You can learn this from a nice book : Mark A. Heald, Jerry B. Marion: Classical Electromagnetic Radiation.

18. May 9, 2013

### DrewD

The classical description doesn't apply if you are considering electrons which would emit radiation due to their acceleration around a loop of wire. I assume it has something to do with indistinguishability of electrons in the conduction band, but I don't know much about solid state physics.