A conducting sphere `A` of radius `a` ,with charge `Q` , is placed concentrically inside a conducting shell `B` of radius `b` . `B` is earthed. `C` is the common centre of the `A` and `B`

Options

A. The field at a distance `r` from `C` , where `a le rle b` , is `k(Q)/(r^(2))`
B. The potential difference between `A` and `B` is `kQ((1)/(b) - (1)/(b))`
C. The potential at a distance `r` from `C`, where `alerleb`, is `kQ((1)/(r ) - (1)/(b))`
D. All options are correct

Answer

4

Explanation

(a) `a le rle b , E = k(Q)/(r^(2))`
(b) `V_(A) - V_(B) = (1)/(4 pi in_(0)) [ { (Q)/(a ) + (-Q)/(b )} - { (Q)/(b ) + (-Q)/(b)}]`
`= (1)/(4 pi in_(0)) Q[ (1)/(a) - (1)/(b)] = kQ((1)/(a) - (1)/(b))`
(c ) `V = (1)/(4 pi in_(0)) [ (Q)/( r ) + (-Q)/( b) = kQ ((1)/(r ) - (1)/(b))`