Electrodynamics : Oscillating Quadrupole

[Clipse]

Homework Statement

Find E for a quadrupole, oscillating sinusoidally. The method suggested is to take two Hertzian dipoles, a distance 'a' apart, and find the superposition of the two. They both have an equal dipole moment, and angular velocity, but have a phase difference of pi between them.

Homework Equations

Oscillating E field for a dipole;

The Attempt at a Solution

I'm just having difficulty trying to visualise how the two out of phase Hertzian dipoles will superpose together. I can kind of see how after doing the correct expansion, terms will disappear as the 1/r and sin terms in the denominator will be negligible compared to those in the phase of the exponent. I just need a more basic outline of how to set the problem up. Any help is much appreciated.

 

[Clipse]

do I just start off saying that the magnetic quadrupole moment is;

p = (Coswt + Sinwt) z?

Edit - made a silly mistake, the angle between them is pi and not pi/2, so it's not sine and cosine, it's just a linear combination of sines.

 

[Onias]

This problem has been confusing me too.