Three concentric metallic shells A, B and C of radii a,b and c (a<b<c) have surface charge densities respectively as shown.
(a) Obtain the expressions for the potential of three shells A, B and C.
(b) If shells A and C are at the same potential, obtain the relation between a, b and c.
(a) We know,
The potential of sphere 'A' is given as,
Where,
then,
Such that, , then
Similarly,
Hence,
Similarly, the potential of sphere 'B' is given as;
Such that, , then
Similarly,
Similarly for ,
(b) we know,
then, the given condition if shell A and C are equal;
On putting the values, we get
such that
c =
- this is the obtained relation between a, b and c.