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Homework Statement
A very long cylinder of linear dialectric material is placed in an otherwise uniform electric field ##E_0##. Find the resulting field within the cylinder. (The radius is ##a##, the susceptibility ##X_e##, and the axis is perpendicular to ##E_0##)
Homework Equations
Boundary conditions
##V_i = V_o## at ##s=a##
##\epsilon \frac{\partial V_i}{\partial n} = \epsilon_0 \frac {\partial V_o}{\partial n}## because there is no free charge
##V = -E_0*s*cos(\theta)## for ##r>>a##
The Attempt at a Solution
I've gotten this far
##\epsilon_r[-na^{-n-1}* (Acos(n*\theta) + Bsin(n*\theta))] = na^{n-1} * (Ccos(n*\theta) + Dsin(n*\theta)) -E_0cos(\theta)##
where n is what I'm summing over. I'm unsure of how to restrict the constants of the trig functions to reduce the problem.