Interference Rate of Radiation of 2 Charges in Circular Motion

Abstract

We present an exact formula for the computation of the interference rate of radiation in the case of two charges revolving with constant angular velocity at opposite ends of a diameter in a fixed circle. The formula is valid for arbitrary velocities of the charges, and can be easily studied by numerical methods, even for velocities very close to the velocity of light. For ultrarelativistic motion, the interference rate of radiation behaves as $\ln(1-v^2/c^2)^{-1/2}$, which contrasts with the behavior $(1 - v^2/c^2)^{-2}$ for the rate of radiation for one charge in circular motion. This is the first exact calculation for the interference rate of radiation of two relativistic charges, and it is useful in connection with the old controversy about the correctness of the Lorentz-Dirac equations of motion for more than one charge.