Question

Two isolated conducting spheres, ${\text{S}}_1$ and ${\text{S}}_2$ of radius $\frac{2R}{3}$ and $\frac{R}{3}$ have $12\mu \text{C}$ and $-3\mu \text{C}$ charges, respectively, and are at a large distance from each other. They are now connected by a conducting wire. A long time after this is done, the charges on ${\text{S}}_1$ and ${\text{S}}_2$ are respectively-

• A. $4.5\mu \text{C}\text{on both}$
• B. $+4.5\mu \text{C}$ and $-4.5\mu \text{C}$
• C. $3\mu \text{C}$ and $6\mu \text{C}$
• D. $6\mu \text{C}$ and $3\mu \text{C}$

Answer 1

The correct option is D $6\mu \text{C}$ and $3\mu \text{C}$



After connecting the isolated conducting spheres, ${\text{S}}_1$ and ${\text{S}}_2$ their potential becomes equal.

$\frac{q_1}{q_2}=\frac{C_1}{C_2}[\because C\propto R]$

$\frac{x}{9-x}=\frac{\frac{2R}{3}}{\frac{R}{3}}$

$\Rightarrow 3x=18$

$\Rightarrow x=6\mu \text{C}$

$\therefore q_1^{{}^{\prime }}=6\mu \text{C}\&q_2^{{}^{\prime }}=3\mu \text{C}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(D\right)$ is the correct answer.