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A solid sphere of radius R has charge q ...

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

A

` R`

B

` R//2`

C

` R//3`

D

` 2R`

Text Solution

Verified by Experts

The correct Answer is:
C
` V_("in") = (KQ) /(2K^3) (3R^2-r^2)`
Potential at center `1(r=0)`
` V_0 = (3 KQ)/(2R)` ....(1)
` V_(out) = 1/2 V_0`
Let at distance `x` from the surface pointial is half of the potential at center . So
` (KQ)/(R+x) = 1/2 (3 KQ)/(2R)` ….(2)
From (1) and (2) ` x= R/3` .
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