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)

$\sigma =\frac{Q_{1}}{4 \pi R^{2}}=\frac{Q_{1}}{4 \pi R^{2}}$
$\sigma =\frac{Q_{2}}{4 \pi \left(2 R\right)^{2}}=\frac{Q_{2}}{16 \pi R^{2}}$
$Q_{B}′=\left(\frac{Q_{1} + Q_{2}}{C_{1} + C_{2}}\right)C_{2}$
$Q_{B}^{′}=\frac{20 \pi R^{2} \sigma \times 2 C}{3 C}=\frac{40 \pi R^{2} \sigma }{3}$
$\sigma ′=\frac{\frac{40 \pi R^{2} \sigma }{3}}{4 \pi \left(2 R\right)^{2}}=\frac{40 \pi R^{2} \sigma }{3 \times 16 \pi R^{2}}=\frac{5 \sigma }{2 \times 3}=\frac{5 \sigma }{6}$