First slide

Pontial due to

Question

A spherical space of radius R is carrying some electric charge uniformly distributed over its entire volume. P is a point inside the sphere at a radial distance r from the centre. If the potential at P is 11/8 times the potential at the surface of the spherical space, then

Moderate

A

$r = \frac{R}{\sqrt{2}}$
B

$r = \frac{R}{2 \sqrt{2}}$
C

$r = \frac{R}{2}$
D

$r = \frac{R}{4}$

Solution

Potential at a radial distance r $(r \leq R)$ is given by $V = \frac{Vs}{2} (3 - \frac{r^{2}}{R^{2}})$
$∴ \frac{11}{8} Vs = \frac{Vs}{2} (3 - \frac{r^{2}}{R^{2}}) \Rightarrow 3 - \frac{r^{2}}{R^{2}} = \frac{11}{4} \Rightarrow r = \frac{R}{2}$

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