Charge Radiation: Acceleration & Constant Charges

[Inquisiter]

How is the fact that ALL accelerating charges radiate reconciled with the fact that the radiation reaction force is ZERO when the acceleration of the charge is CONSTANT??

Also, if you are accelerating, but the charge is NOT, do you see any radiation coming from the charge or not?


Thanks

 

[shyboy]

the radiation force is not zero. Tthe part of the radiation force which is propotional to the acceleration is combined wth the inertia force.
If you are accelerating, then you will see oscillating electromagnetic field, so you should see a radiation.

 

[Inquisiter]

the radiation force is not zero. Tthe part of the radiation force which is propotional to the acceleration is combined wth the inertia force.
If you are accelerating, then you will see oscillating electromagnetic field, so you should see a radiation.

So does that mean that when the acceleration is constant the charge radiates but the radiation doesn't go off to infinity, but rather stays with the charge (in the charge's field)? What if in your frame of reference the charge is undergoing constant DEceleration? Now the charge is doing work on whatever is decelerating it, that energy has to come from somewhere, does that mean that the radiation(i.e. the Poynting vector) is directed TOWARD the charge? But if the acceleration is not constant, then I guess the radiation goes off to infinity and can't be recovered? Ok, this doesn't seem right... The radiation field is proportional to 1/r. But if the acceleration is constant, it's still proportional to 1/r, right? So the radiation DOES go off to infinity, otherwise I'd think that it would be proportional to 1/r^2.

 

[shyboy]

OK, thre is so called Larmor formula for a linearly accelerated nonrelativistic charge

$$P=\frac{1}{4\pi \epsilon_0}\frac{2e^2\ddot x^2}{3c}$$

Larmor formula is applicable for acceleration in arbitrary direction to the velocity