Problem 11 (14 points) - Boundary Value Problem A capacitor is made with a spherical PEC surface of radius a centered at the origin inside a larger spherical PEC surface of radius b also centered around the origin. A potential of V, is applied to the inner sphere, and the outer sphere is grounded (V = 0). a) (5 points) Find the general solution of the spherical Laplace equation for the space between the two spheres. b) (2 points) State the two boundary values for the space between the two spheres. c) (2 points) Solve for the coefficients in the general solution from part a) using the boundary values in part b). d) (4 points) Use the normal electric boundary condition to find the surface charge density on the inner sphere, then find the total charge on the inner sphere. e) (1 points) Calculate the capacitance of the spherical capacitor.

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