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azupol
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Homework Statement
A thin spherical shell of radius R carries a surface charge density of the form
[itex]
kcos3 \theta
[/itex]
Find the electric field inside and outside the sphere and demonstrate explicitly that its
components satisfy the relevant boundary conditions at the surface.
Homework Equations
The solution to Laplace's Equation in spherical coordinates :\Sigma Al rl Pl(cos \theta) (r≤R)\Sigma Bl r-(l+1)Pl(cos \theta) (r≥R)
The Attempt at a Solution
I worked it through untilAl= k/2ε0Rl-1∫cos3 \theta Pl cos \theta sin \theta d \thetaWhere do I go from here? Do I only need to consider the third Legendre polynomial?i.e.##(5cos3\theta - 3 cos \theta)/2 ##
Are all the other coefficients zero?
EDIT: It seems TeX does not want to work for me, but I'm sure you get the idea
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