A sphere of radius a has V = 0 everywhere except between 0 < θ < π/2 and 0 < φ < π. Write an expression in spherical harmonics for the potential for r > a. For which values of m are there contributions? Determine the contributions through l= 2. How could you determine the leading contribution using just superposition?
Again I will be uploading images. I am only looking for answer in terms of a general formula. Not a fully drawn out calculation.
The Attempt at a Solution
I will be uploading a solution. Again the solution they are looking for is very general. What I am confused about is that this problem implies that for certain values of m there are no contributions but that does not seem to be the case with these bounds of integration. Also I do not understand the superposition part of this question.