Monopole and Dipole Terms of Electric potential (V) on Half Disk

jkthejetplane
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Homework Statement
So this is from my last exam. I wanted to figure this out as we can get some credit back on a question plus finals are coming up.
Relevant Equations
On my attached attempt you can see the equations I use as well as a few of the professor's notes
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Physics news on Phys.org
Calculate potential on the z axis in terms of a Legendre polynomials. Then the off axis expansion will follow.
 
(a) The polarisation pattern is elliptical with maximum (1,1) and minimum (-1,-1), and anticlockwise in direction. (b) I know the solution is a quarter-wave plate oriented π/4, and half-wave plate at π/16, but don't understand how to reach there. I've obtained the polarisation vector (cos π/8, isin π/8) so far. I can't find much online guidance or textbook material working through this topic, so I'd appreciate any help I can get. Also, if anyone could let me know where I can get more...

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