A small conducting 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(Q gt q)` and are insulated from each other. The potential difference between the spheres will be

Options

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

Answer

3

Explanation

`V_(A) = (1)/(4 pi in_(0)) [ (q)/( r) + (Q)/(R )]`
`V_(B) = (1)/(4 pi in_(0)) [ (q)/(R ) + (Q)/(R )]`
`V_(A) - V_(B) = (1)/(4 pi in_(0)) [ (q)/(r ) - (q)/(R )]`