A non conducting sphere of radius R is charged uniformly. At what distance from its surface is the electrostatic potential is half the potential at its centre ?

Options

A. R
B. R/2
C. R/3
D. 2R

Answer

C

Explanation

The potential at the centre of the sphere
`V_(C ) = (1)/(4pi epsilon_(0))(3Q)/(2R)`
We require a point where `V = (V_(C ))/(2) = (1)/(4pi epsilon_(0))(3Q)/(4R)`
This point cannot be inside the sphere where `V ge (1)/(4pi epsilon_(0))(Q)/(R )`
Let the point be outside the sphere at a distance r from the centre. Then
`V = (1)/(4pi epsilon_(0))(Q)/(r ) = (1)/(4pi epsilon_(0))(3Q)/(4R) :. r = (4)/(3)R`
Distance from the surface `= r - R = (4)/(3)R - R = (R )/(3)`