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There are four concentric shells A,B, C ...

There are four concentric shells A,B, C and D of radii `a,2a,3a` and `4a` respectively. Shells B and D are given charges `+q` and `-q` respectively. Shell C is now earthed. The potential difference `V_A-V_C` is `k=(1/(4piepsilon_0))`

A

` (Kq)/(2a)`

B

`(kKq)/(3a)`

C

`(Kq)/(4a)`

D

`(kq)/(6a)`

Text Solution

Verified by Experts

The correct Answer is:
D

(i) Since shall `A` is isoleted so it will not have any charge.
(ii) Since cell `C` is Earthed os ` V_c =0`
(iii) From Gauss theorem inner face of `C` will have `-q` charge whil outer face will have ` +q` charge so
`V_A -V_c =- int_(2a)^(3a) vec E. vec (dr)`
put` E =0` for a to ` 2a`
and `E=(Kq)/r^2 ` for 2a to 3a
`V_A-V_c =- int _(2a)^(3a) (Kq)/r^3 dr= (Kq)/(6a)`.
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