Three concetric sphereical metal shells A,B,C or radii a,b,c (c gt b gt a) have surface charge densities +sigma , - sigma and +sigma respectively. (a) Findthe potentialsof thethree shells? (b) If theshells A and Care at same potential , find therelation between a,b and c.

Three concetric sphereical metal shells A,B,C or radii a,b,c (c gt b g

1.	Three concetric sphereical metal shells A,B,C or radii a,b,c (c gt b gt a) have surface charge densities +sigma , - sigma and +sigma respectively. (a) Findthe potentialsof thethree shells? (b) If theshells A and Care at same potential , find therelation between a,b and c.
Answer» Solution :(a) Chargeson the three SHELLS are `q_(A) + + sigma 4pia^(2)` `q_(B) = - sigma 4 PI b^(2)` `q_(B)= -sigma 4 oi b^(2)` `q_(C) = + sigma 4 pi c^(2)` `V_(A) = (1)/(4 pi in_(0)) {(q_(A))/(a) + (q_(B))/(b) + (q_(c))/(c)} = (sigma)/(in_(0)) (a+b+c)` `V_(B) = (1)/(4 pi in_(0)) { (q_(A))/(b) + (q_(B))/(b) + (q_(c))/(c)} = (sigma)/(in_(0)) ((a^(2)-b^(2))/(b) + c)` `V_(c)= (1)/(4PI in_(0)) {(q_(A))/(c) + (q_(B))/(c) + (q_(C))/(c)} = (sigma)/(in_(0))((a^(2) - b^(2) + c^(2))/(c))` (b) If `V_(A) = V_(C)` , on substitution . we geta+ b = c