Question

Two concentric shells A and B of radii R and 2R are charged to potential 2V and
respectively. Now shell B is earthed and let the charges on them becomes
and ge. Then potential difference between A and B after earthing becomes
3V
2
B
A
NlW
V
2
3​

Answer 1

Given:

Two concentric shells A and B of radii R and 2R are charged to potential 2V and respectively. Now shell B is earthed and let the charges on them becomes and ge.

To find:

Then potential difference between A and B after earthing becomes

Solution:

From given, we have,

Charges before shell B is earthed = qA andqB

Charges after shell B is earther = qA' and qB'

Now consider, the potential of A

V = qA/R + qB/2R   ..........(1)

Now consider, the potential of B

3V/2 = qA/2R + qB/2R  ....(2)

solving (1) and (2), we get,

qA/qB = 1/2

Now consider, when shell B is earthed, VB' = 0

⇒ qA'/2R + qB'/2R = 0

⇒ qB' = - qA'

|qA'| / |qB'| = 1

VA' = qA'/R + qB'/2R

∴ VA' = qA'/2R

The potential difference between A and B:

VA' - VB' = VA - VB = 2V - 3/2V = 1/2V

∴ VA' = 1/2 V since VB' = 0