Question

A sphere of $4cm$ radius is suspended within hollow sphere of $6cm$ radius. The inner sphere is charged to a potential $3esu$, when the outer sphere is earthed. The charge on the inner sphere is :

• A. 54 esu
• B. 27 esu
• C. 30 esu
• D. 36 esu

Answer 1

Answer: (D)

The sphere of radius $=4cm=4\times 10^{-2}m$
hollow sphere $=6cm=6\times 10^{-2}m$
inner sphere charged to a potential $3$ e.s.u.
lesu $=300V$
lesu $=3\times 10^{-10}C$
Let, Charge on inner sphere is $+Q$, then, $-Q$ is induced in the surface of outer sphere.
Now, potential on inner sphere $=\frac{Q_1}{r_1}+\frac{Q_2}{r_2}$
Here, $Q_1$ is the charge on inner sphere.
$r_1$ is the radius of inner sphere.
$Q_2$ is the charge on outer sphere.
$r_2=$ the radius of the outer sphere.
Given, Potential on inner sphere $=3$ esu of potential
$r_1=4cm$
$r_2=6cm$
$3$ esu $=\frac{Q}{4}-\frac{Q}{6}$
$\Rightarrow Q\left[\frac{1}{4}-\frac{1}{6}\right]=3$
or, $\frac{Q}{12}=3$
or, $Q=36$ esu
Hence, charge $=36$ esu of charge.