Electrodynamics - finding potential of a non conducting shell

[jerry222]

Homework Statement

Consider a spherical, charged, non-conducting shell of radius R. Given "surface potential", find potential at any distance.

I do realise there might be such a thing as a surface potential but how can i relate it to R, the distance? Am i supposed to solve the laplace equation with the given surface potential as a solution? I'm a bit stuck, appreciate any hint

Relevant Equations

$\Del V = 0$

 

[Philip Koeck]

Homework Statement:: Consider a spherical, charged, non-conducting shell of radius R. Given "surface potential", find potential at any distance.

I do realise there might be such a thing as a surface potential but how can i relate it to R, the distance? Am i supposed to solve the laplace equation with the given surface potential as a solution? I'm a bit stuck, appreciate any hint
Relevant Equations:: $\Del V = 0$

View attachment 323688

Have you tried part (b) first?
From the answer to that you should be able to get the answer to (a) if the integral is not too nasty.

 

[TSny]

Am i supposed to solve the laplace equation with the given surface potential as a solution?

Yes. My hint would be to notice that the potential on the surface of the sphere, that you are given, can be expressed as the sum of just a few Legendre polynomials with certain coefficients. Then compare to the general solution of Laplace's equation in spherical coordinates for problems with azimuthal symmetry. Hopefully, you're familiar with equation (14) here.