Question

Two concentric shells of radii 1 cm and 2 cm are charged to 3V and 5V, respectively. The charge on the inner shell is

• A. $-\frac{4}{9}\times {10}^{-11}C$
• B. $\frac{4}{9}\times {10}^{-11}C$
• C. $-\frac{2}{9}\times {10}^{-11}C$
• D. $\frac{2}{9}\times {10}^{-11}C$

Answer 1

The correct option is A

$-\frac{4}{9}\times {10}^{-11}C$

$\frac{K{Q}_1}{{10}^{-2}}+\frac{K{Q}_1}{2\times {10}^{-2}}=3V$

$\Rightarrow 2Q_1+Q_2=\frac{2}{3}\times {10}^{-11}\dots \left(i\right)$

$\frac{K{Q}_1}{2\times {10}^{-2}}+\frac{K{Q}_2}{2\times {10}^{-2}}=5V$

$\Rightarrow Q_1+Q_2=\frac{10}{9}\times {10}^{-11}\dots \left(ii\right)$

From (i) and (ii)

$Q_1=-\frac{4}{9}\times {10}^{-11}C$