Question

Two isolated metallic solid spheres of radii $R$ and $2 R$ are charged such that both have same charge density $\sigma$. The spheres are then connected by a thin conducting wire. If the new charge density of the bigger sphere is $\sigma^{\prime}$ The ratio $\frac{\sigma^{\prime}}{\sigma}$ is :

• A. $\frac{5}{3}$
• B. $\frac{9}{4}$
• C. $\frac{5}{6}$
• D. $\frac{4}{3}$

Answer 1

Answer: (C)

$\frac{5}{6}$

Answer 2

4πε0​RQ1′​​=4πε0​(2R)Q2′​​
∴Q2′​=2Q1′​
Q1′​+Q2′​=Q1​+Q2​
∴2Q2′​​+Q2′​=20πR2σ
23​Q2′​=20πR2σ
∴4π(2R)2Q2′​​=32​⋅16πR220πR2σ​
∴σσ′​=65​