Question

A total charge Q is given to (Two concentric shells) so that their surface charge densities are equal. Deduce an expresion for potential at their common centre. ​

Answer 1

Explanation:

Let charge on surface of sphere of radius R be q

A

and charge on surface of sphere of radius r be q

B

Since there surface charge densities is equal

R

2

q

A

=

r

2

q

B

and

q

A

+q

B

=Q

on solving both the equations we get

q

A

=

R

2

+r

2

QR

2

q

B

=

R

2

+r

2

Qr

2

potential at the common center will be

V=

R

kq

A

+

r

kq

B

V=

(R

2

+r

2

)

kQ(R+r)

V=

4πϵ

o

(R

2

+r

2

)

Q(R+r)