Question

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

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

Answer 1

Answer: (C)

$R/3$

We know,

The potential at an point inside the insulating sphere is given by,

$V_r=\frac{kQ}{2R}(3-\frac{r^2}{R^2})$

$\therefore V_o=\frac{3kQ}{2R}$

Also for a point outside the surface,

$V_p=\frac{kQ}{R+r}$

We know, $V_o=2V_p$

$\therefore \frac{3kQ}{2R}=2\frac{kQ}{R+r}$

$\therefore r=\frac{R}{3}$