A small conducing sphere of radius r is lying concentrically inside a bigger hollow conducting sphere of radius R . The bigger and smaller spheres are charged with Q and q `(Qgtq)` and are insulated from each other . The potential difference between the spheres will be

Options

A. `(1)/(4piepsilon_(0))((q)/(r)-(Q)/(R))`
B. `(1)/(4piepsilon_(0))((Q)/(R)+(q)/(r))`
C. `(1)/(4piepsilon_(0))((q)/(r)-(q)/(R))`
D. `(1)/(4piepsilon_(0))((q)/(R)-(Q)/(r))`

Answer

C

Explanation

The potential of Q at the surface A
`(1)/(4piepsilon_(0))*(Q)/(R)`.
The potential of q at the surface A
`=(1)/(4piepsilon_(0))*(q)/(R)`.
The potential at B is due to Q inside
`(1)/(4piepsilon_(0))*(Q)/(R)`.
The potential at B due to `q=(1)/(4piepsilon_(0))*(q)/(r)`.
`therefore` Potential at `A,V_(A)=(1)/(4piepsilon_(0))((Q)/(R)+(q)/(R))`,
Potential at `B,V_(B)=(1)/(4piepsilon_(0))((Q)/(R)+(q)/(r))`.
`thereforeV_(B)-V_(A)=(1)/(4piepsilon_(0))*((q)/(r)-(q)/(R))`