Question

Example 17. Three concentric metallic shell A,B and C
of radii, and c(a<b<c) have surface charge densities
+sigma,-sigma and a respectively.
(a) Find the potentials of three shell A,B and C
(a) If the shells A and C are at the same potential
obtain the relation between a,b,c.​

Answer 1

V

A

=

4πϵ

0

a

σ4πa

2

+

4πϵ

0

b

(−σ)4πb

2

+

4πϵ

0

c

σ4πc

2

=

ϵ

0

σ

(a−b+c)

Similarly, V

C

=

ϵ

0

σ

(

c

a

2

−

c

b

2

+c)

But V

A

=V

C

a−b+c=

c

a

2

−b

2

+c

Therefore, a+b=c