Question

A large hollow metallic sphere $A$ (of radius $R$ ) is positively charged to a potential of $100\text{V}$ and a small sphere $B$ (of radius $\frac{R}{5}$) is also positively charged to a potential of $100\text{V}$. Now $B$ is placed inside $A$ and they are connected by a wire. The final potential of $A$ will be:

• A. $200\text{V}$
• B. $150\text{V}$
• C. $120\text{V}$
• D. none of above

Answer 1

The correct option is C $120\text{V}$

The charge on sphere $A$ and $B$ is :
$V=\frac{1}{4\pi {ϵ}_0}\frac{q}{r}$

$\therefore q_A=\left(4\pi {ϵ}_{0}R\right)V$
and $q_B=\left(4\pi {ϵ}_0\right)\frac{R}{5}V$
When they are connected by conducting wire, the entire charge will flow to outer sphere, so that their potentials become equal. Thus
$q=q_A+q_B=\left(4\pi {ϵ}_0\right)\frac{6R}{5}.V$
The final potential of $A$ now,
$V^{\prime }=\frac{1}{4\pi {ϵ}_0}\frac{q}{R}=\frac{\left(4\pi {ϵ}_0\right)\left(\frac{6R}{5}V\right)}{4\pi {ϵ}_{0}R}$
$=\frac{6V}{5}=\frac{600}{5}=120\text{V}$