- #1

fluidistic

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## Homework Statement

; attempt and equations[/B]Many times I face problems with a wire loop with some current (which may or may not depend on time, which may or not move) "flowing" in it. And I'm asked to calculate the radiation due to it.

So using the multipole expansion I know that the dominant terms in the radiation will be the electric dipole term, followed by the magnetic dipole term and then the electric quadrupole terms, assuming they are non-zero.

So the first thing to do is to calculate the electric dipole term which is worth ##\vec p = \int \vec r \rho (\vec r ) dV##. And here is my question. Is this electric dipole term always worth 0, because there's no rho? Or must I imagine that there's a rho because there's a current?

In an exam (where I had a circular current loop with ##I(t)=I_0 \cos (\omega t)##), I wrote down that rho=0 so that p(t)=0 and so that there's no radiation due to the electric dipole term. I then went on to calculate the magnetic dipole term (which was non zero) and calculated the radiation due to it. But I was awarded 0 credit whatsoever, because the professor did not buy my explanation for ##\vec p (t) =\vec 0## even though it is true that ##\vec p(t)=\vec 0##. He told me I could have used the continuity equation ##\nabla \cdot \vec J + \frac{\partial \rho}{\partial t}=0## to show that this moment vanishes (which really complicates things a lot).

So I wonder whether I'm correct to assume that rho=0 or not. And if there's a quick way to show that ##\vec p (t)## vanishes for set up like these.