# The force required to accelerate a radiating charge

1. Oct 25, 2012

### blgeo

If we try to treat a non-relativistic point charge, what force do we need to accelerate it uniformly, when we take the fact that it radiates into account? I assumed the force would do the necessary extra work so that:

F dx = d(1/2 mv^2) + P dt;

where P is the Larmor power, but at any point where the velocity is 0 this would imply an infinite force. What am I missing?

2. Oct 26, 2012

### AJ Bentley

You've got the cart in front of the horse.

The emitted radiation is a very, very small drag force on the electron, not the accelerating force, which usually comes from an applied electric or magnetic field.

3. Oct 26, 2012

### andrien

4. Oct 28, 2012

### blgeo

I'm assuming a case with no 'jerk' (constant acceleration), and I would like to figure out what force we need to put in in order to achieve this - I'm aware the radiation is effectively a small drag on the electron, but what is the required additional input force to keep acceleration constant, and conserve energy? I don't think Abraham Lorentz is much help as this applies to non-constant a. How do we conserve energy when a dot = 0?

5. Oct 30, 2012

### andrien

In case of no jerk,you can see there is zero radiation reaction force but you also know that an accelerating charge radiates,so there is supposed to be some force putting energy into it.But the problem is from where it will come because radiation reaction is zero for constant acceleration.You can see for this dilemma here
http://www.mathpages.com/home/kmath528/kmath528.htm

6. Oct 31, 2012

### blgeo

Just what I was looking for - thanks andrien