Question

A metallic sphere of radius $R_1$ is charged to a potential V. If it is enclosed by a spherical conducting shell of radius $R_2$ and connected to it, its new potential will be

• A. Zero
• B. $V\left(\frac{R_1}{R_2}\right)$
• C. $V\left(\frac{R_2}{R_1}\right)$
• D. $V\left(\frac{R_1}{R_1+R_2}\right)$

Answer 1

The correct option is B $V\left(\frac{R_1}{R_2}\right)$

If Q is the charge on the metallic sphere, its potential is given by $V=\frac{1}{4\pi {ϵ}_0}\frac{Q}{R_2}$. All points inside the spherical shell will be at this potential. Hence, the new potential of the metallic sphere will also be $V^{{}^{\prime }}$
$\therefore \frac{V^{{}^{\prime }}}{V}=\frac{R_1}{R_2}$ $\therefore V^{{}^{\prime }}=V\left(\frac{R_1}{R_2}\right)$