Question

Two conducting and concentric thin spherical shells or radii $a$ and $b,\left(b>a\right)$ have charges $q_1$ and $q_2$ respectively. Now if the inner shell is earthed then the final charge on this shell will be

• A. $\frac{q_2{a}^2}{b^2}$
• B. $\frac{-q_{2}a}{b}$
• C. $\frac{\left(q_1+q_2\right)}{2}$
• D. $-\frac{q_{2}b}{a}$

Answer 1

The correct option is B $\frac{-q_{2}a}{b}$

$\therefore$ The inner spherical conductor is grounded, $\Rightarrow$ potential, $V=0$

Also, Potential at inner shell,

$V=\frac{K{Q}_1}{a}+\frac{{KQ}_2}{b}$

$\Rightarrow O=\frac{K{Q}_1}{a}+\frac{{KQ}_2}{b}$

$Q_1=\frac{-Q_{2}a}{b}$

$\therefore$ Charge on inner shell $Q_1=\frac{-Q_{2}a}{b}$

Option (B) is the correct option.