# Accelerating charged particles emit EM waves?

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1. Apr 21, 2012

### plazprestige

I know that if you have alternating current in a wire, it will produce electromagnetic waves since the electric and magnetic field change direction continuously as the wave propagates, and that the wave direction, orientation of the E component, and orientation of the B component will all be mutually perpendicular.

However, this acceleration arises from changing direction of charged particles, not speed.

My question is this:

If I were to accelerate an electron by increasing its speed in one dimension (+x), would that electron emit EM waves?

The electron will have a constant electric field pointing towards itself, and its magnetic field will be going into the page in the 1st quadrant and going out of the page in the 4th quadrant, and the magnitude of the magnetic field will be increasing.

I can visualize the mutually perpendicular B and E waves, but they would not be changing orientation continuously since it isn't AC current. Would this still be an EM wave?

2. Apr 22, 2012

### nonequilibrium

Hello,

(For the case of uniform acceleration (at all times!) it's a bit controversial, the theory is not clear on its prediction, or perhaps it depends on what you mean by radiation in that case, but the example is pathological so never mind for now)

I don't really follow what you say next though. I think you're having some misconceptions. For example "The electron will have a constant electric field pointing towards itself" is not really correct: the electric field is retarded (due to the fact that the electric field spreads out at a finite speed), e.g. see http://www.cco.caltech.edu/~phys1/java/phys1/MovingCharge/MovingCharge.html

Also "but they would not be changing orientation continuously" doesn't sound correct: the electric field and magnetic field are changing in time, aren't they? This is simply due to their source changing in time.

3. Apr 22, 2012

### plazprestige

I'm a bit confused then. An electron will have electric field lines pointing toward itself (since convention has positive test charges in the field). As the electron speeds up, its electric field will not change directly since its charge is the same, but its magnetic field will increase in magnitude.

Would this increasing magnetic field induce an increasing electric field?

Even if the answer to the above is yes, I still do not see how an electron simply speeding up will produce EM waves in the nature of which alternating current produces EM waves.

4. Apr 22, 2012

### nonequilibrium

"I'm a bit confused then. An electron will have electric field lines pointing toward itself"

Did you not fully read my last point? I addressed this misconception.