A solid sphere of radius R has charge q uniformly distributed over its volume. The distance from it surfce at which the electrostatic potential is equal to half of the potential at the centre is

Options

A. `R`
B. `(R )/(2)`
C. `(R )/(3)`
D. `2 R`

Answer

3

Explanation

At centre :
`V_(1) = (1)/(4 pi in_(0)) (3Q)/(2 R)`
At distance `r` from centre `(r gt R)`
`V = (1)/(4 pi in_(0)) .(Q)/(r )`
`V = (1)/(2) V_(1)`
`(1)/(4 pi in_(0)) . (Q)/( r) = (1)/(2) .(1)/(4 pi in_(0)) .(3Q)/(2 R)`
`(1)/(2) = (3)/(4 R) rArr r = (4 R)/(3)`
Distance from surface , `r - R = R//3`