Maxwell's Equations, Yet Again

Suppose we are given a system of classical charges that oscillate harmonically with time. Note that, as before, this can be viewed as the special case of the Fourier transform at a particular frequency of a general time dependent distribution; however, this is a very involved issue that we will examine in detail later in the semester.

The form of the charge distribution we will study for the next few weeks is:

$$\rho(\vx,t) = \rho(\vx) e^{-i \omega t}$$ (13.1)

$$\vJ(\vx,t) = \vJ(\vx) e^{-i \omega t} .$$ (13.2)

The spatial distribution is essentially ``arbitrary''. Actually, we want it to have compact support which just means that it doesn't extend to infinity in any direction. Later we will also want it to be small with respect to a wavelength.