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

Answer

A, B, D

Explanation

Let charge `q_1` comes from the earth on outer shell
`q_1=-Q`
`1/(4piepsilon_0)[Q/(2r+q_1/(2r))]=0`
or `q_1=-Q`
When `S_2` is closed and opened
`V_("inner" )=0`
`:. 1/(4piepsilon_0)[q'_1/r-Q/(2r)]=0`
`or `q_1^'=Q/2`
proceeding in the similar manner after n such operations we get,
Charge on the inner shell,
q_(n)^' =Q/((2)^n)`
and the potential difference between the shells
`/_\V=q_(n)^'/(4piepsilon_0) (1/r-1/(2r))`
`/_\V-1/(2)^(n+1) [Q/(4piepsilon_0r)]`