Given two two grounded concentric spherical shells with radii a,b (a<b) and a point charge q between them at a<r=R<b find:
1.The surface charge density of the point charge using the delta function, assume the charge is on the z axis
2.By using the separation of variables method find the electric potential between the shells.
I have no idea how to insert mathematical equation in the forum but the most relevant equations are the jump discontinuity in the orthogonal part of the field and the general form of the solution of the Laplace equations in spherical coordinates
The Attempt at a Solution
In my first try I tried to solve for the whole volume at once which produced contradictions, in my second attempt I divided the volume and solved for each volume seperately but I got stuck on the orthogonality condition for the Legendre polynomials, the precise attempt is shown in the images