Question

Two isolated metallic spheres of radii $R$ and $2R$ are charged such that both of these have same charge density $\sigma$ . These sphere are located far away from each other and connected by a thin conducting wire, the new charge density on the bigger sphere -

• A. $\frac{3\sigma }{2}$
• B. $\frac{5\sigma }{6}$
• C. $\frac{6\sigma }{5}$
• D. $\frac{2\sigma }{3}$

Answer 1

Answer: (B)

$\sigma =\frac{Q_1}{4\pi R^2}=\frac{Q_1}{4\pi R^2}$
$\sigma =\frac{Q_2}{4\pi {\left(2R\right)}^2}=\frac{Q_2}{16\pi R^2}$
$Q_B\prime =\left(\frac{Q_1+Q_2}{C_1+C_2}\right)C_2$
$Q_B^{\prime }=\frac{20\pi R^2\sigma \times 2C}{3C}=\frac{40\pi R^2\sigma }{3}$
$\sigma \prime =\frac{\frac{40\pi R^2\sigma }{3}}{4\pi {\left(2R\right)}^2}=\frac{40\pi R^2\sigma }{3\times 16\pi R^2}=\frac{5\sigma }{2\times 3}=\frac{5\sigma }{6}$