Consider a hollow sphere of radius R placed in a vacuum. The sphere has a surface charge density of σ (R, 0) = (3 cos² 0-1). 2 The general solution to Laplace's equation is Bi V(r,θ) = Σ(Apr! + Σ(Ar' + Pi(cost) pl+1. 1=0 a) Write down all of the boundary conditions. Using the boundary conditions:
Using the boundary conditions: b) Find the general solutions for for r<R and for r>R c) Show that, for all I, d) Show that for all I but I-n and find n. V(r, 0) B₁ = R²+¹ Al A₁ = B₁ = 0
e) Find f) Write down the final expressions for inside and outside the sphere. An, Bn V(r, 0)
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