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There are two concentric spherical shell...

There are two concentric spherical shell of radii r and `2r`. Initially, a charge Q is given to the inner shell and both the switches are open.

The twio steps of the above two problems are repeated b times, the potential differences between the shells will be

A

`1/2^(n+1)[Q/(4piepsilon_0r)]`

B

`1/2^n[Q/(4piepsilon_0r)]`

C

`1/2^n[Q/(4piepsilon_0r)]`

D

`1/2^(n-1)[Q/(2piepsilon_0r)]`

Text Solution

Verified by Experts

The correct Answer is:
A
After two steps charge on inner shell remais `Q/2` or half.
so, after n times
`q_("in")=Q/((2))^n)`
Now, according to the principle of generator, potential differece depends on the inner charge only.
`:. PD=q_("in")/(4piepsilon_0)[1/r-1/(2r)]`
`=1/2^(n+1) [Q/(4piepsilon_0r)]`
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