Consider the capacitor formed by a conducting sphere with radius R1 surrounded by a concentric conducting spherical shell with inside radius R2 and outside radius R3.
(1) Calculate the potential of the outer shell when charge Q is put on it and the inner shell is grounded.
(2) Calculate the potential of the inner shell when charge Q is put on it and the outer shell is grounded.
(3) Calculate the charge on the outer sphere when it is grounded and the inner sphere is at potential V.
(4) Convert your calculations above into the coefficients of capacitance---a.k.a. the capacitance tensor.
(5) Convert your calculations above into the potential coefficients---a.k.a. the potential tensor.
There can be some small variety in the definitions of potential and capacitance tensors.
As you have not written the definitions you use, I had to choose some, and chose the potential tensor P to be defined by equation V_i = sum_j P_ij Q_j
and the capacitance tensor as C = inverse of P.
If your ...
Solution sets out the steps to find various things about a spherical shell capacitor, including potential of the shells, charge to the outer sphere and coefficients of capacitance.