Electric Dipole Radiation from a Spinning Current Loop

[khfrekek92]

Homework Statement

Hi everyone,

My problem is fairly simple: We have a circular current loop enclosing area A, and with a constant current I. The loop is rotating about its diameter at a constant angular frequency $$\omega$$. All we need to do is find the electric dipole, and magnetic dipole radiation fields.

Homework Equations

$$\vec{m}=IA \hat{n}=IA(cos(\omega t) \hat{x}+sin(\omega t) \hat{y})$$

$$\vec{p}=\int \rho (r',t) r' d^3 r'$$

The Attempt at a Solution

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For this particular problem, the magnetic dipole moment is very easy to find:
$$\vec{m}=IA \hat{n}=IA(cos(\omega t) \hat{x}+sin(\omega t) \hat{y})$$

Then using this you can easily plug it into the formulas outlined by Jackson to find the B, H, S fields corresponding to magnetic dipole radiation.

However, my problem is the electric dipole moment. How would you go about finding this? There are no "charge densities" moving around in time, only current distributions..

Thanks in advance!

 

[mfb]

This might be too easy, but what would be wrong with a dipole moment of zero?