Question

A metal sphere having a radius $r_{1}$ charged to a potential $V_{1}$ is enveloped by a thin-walled conducting spherical shell of radius $r_{2}$. Determine the potential $V _{2}$ acquired by the sphere after it has been connected for a short time to the shell by a conductor.

• A. $\frac{V_{1} r_{2}}{r_{1}}$
• B. $\frac{V_{1} r_{1}}{r_{2}}$
• C. $V _{1}$
• D. $\frac{V_{1}\left(r_{1}+r_{2}\right)}{r_{2}}$

Answer 1

Answer: (B)

Charge on the metal sphere : $v_{1}=\frac{k q}{r_{1}}$
$\Rightarrow q=\frac{v_{1} r_{1}}{k} .$
On connecting the sphere with shell, entire charge will be transferred to the shell. So, potential of sphere now is
$V _{2}=\frac{ kq }{ r _{2}}=\frac{ V _{ r } r _{1}}{ r _{2}}$