self interaction, conserving energy

jostpuur

I've learned that you cannot deal with the interaction of a charge with its own field in classical electromagnetism. It is said, that this is simply the case with classical theory, and you have to deal with it. But how can this be? If accelerating charge is giving energy to the field, then it should be losing energy itself, but how can it lose energy if it doesn't feel its own field? Is the energy really conserved in classical theory, when one attempts to explain the radiation?

I have never seen an equation, that would tell strictly, what kind of acceleration a charge would suffer with a given rate of change of momentum. I mean, that at least the rate of change of the speed should be less than if particle had no charge. How much less, precisly?

Andrew Mason

Electron self-interaction seems to be one of those aspects of physics that has no right answer, just different ways of looking at it. Feynman spent his life trying to analyse electron self - interaction using retarded potentials, advanced potentials and half-retarded, half-advanced and could not find a solution. See his nobel lecture.

AM

pmb_phy

There is a section in Jackson's 3rd Edition of his EM text. That section is called "Radiative Reaction Force from Conservation of Energy."

Seek your aswer there. Leave it to say that there is an additional force to overcome which is caused by the attempt to accelerate the charged particle. This is known as the Abraham-Lorentz self-force. This is a complex subject and has some quirks to it and I don't know the subject well enough to explain it solidly to others. I recommend that you look this up, perhaps at the library or a search on Google.

Pete