Question

Two concentric spheres of radius $R$ and $2R$ have charges Q and $2Q$. The potential at a point P situated at a point 3R/2 distance from common centre is $V$, Now if outer sphere is earthed, the potential at point P is :

• A. $V/5$
• B. $V/10$
• C. $V/3$
• D. $V$

Answer 1

The correct option is B $V/10$

Before earthing,the potential at P, $V_p=K[\frac{2Q}{3R}+\frac{2Q}{2R}]=V$

so, $\frac{5}{3}\frac{KQ}{R}=V\Rightarrow \frac{KQ}{R}=\frac{3V}{5}$

After earthing the outer sphere, negative charge equal in magnitude to that present on the outer surface of smaller one will be induced on the inner surface of larger one.

$\therefore$ potential at P, $V^{\prime }=K[\frac{2Q}{3R}-\frac{Q}{2R}]=\frac{KQ}{6R}=\frac{3V}{5}\times \frac{1}{6}=\frac{V}{10}$