Question

A solid conducting sphere of radius $10\text{cm}$ is enclosed by a thin metallic shell of radius $20\text{cm}$. A charge $q=20\mu \text{C}$ is given to the inner sphere. Find the heat generated in the process, the inner sphere is connected to the shell by a conducting wire-

Answer 1

On connecting the inner sphere to the outer-sphere, the entire amount of charge will shift to the outer sphere.

Heat generated during the process is,
$\Delta H=U_i-U_f=\frac{q^2}{8\pi {\epsilon }_0{R}_1}-\frac{q^2}{8\pi {\epsilon }_0{R}_2}[\because U=\frac{Q^2}{8\pi {\epsilon }_{0}R}]$

Here $R_1=10\text{cm},R_2=20\text{cm}$

$\Delta H=\frac{(20\times {10}^{-6}{)}^2\times 9\times {10}^9}{2}[\frac{1}{0.10}-\frac{1}{0.20}]$

$\therefore \Delta H=9\text{J}$

Accepted answers : $9,9.0,9.00$