Question

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)]`

Answer 1

Correct Answer - 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)]`