Question

Charge $Q$ is distributed on two metallic spheres having radii $R$ and $3R$ such that both spheres have equal charge density then charge on smaller sphere is

• A. $\frac{Q}{10}$
• B. $\frac{Q}{9}$
• C. $\frac{9Q}{10}$
• D. $\frac{10Q}{11}$

Answer 1

The correct option is A $\frac{Q}{10}$

Spheres have equal charge density
${\sigma }_1={\sigma }_2$
$\Rightarrow \frac{q}{4\pi R^2}=\frac{Q-q}{4\pi (3R{)}^2}$$(\because$ combined charge on both the spheres is $Q)$
$\Rightarrow 9q=Q-q$
$\Rightarrow q=\frac{Q}{10}$