 # Two isolated conducting spheres S1 and S2 of

Question:

Two isolated conducting spheres $S_{1}$ and $S_{2}$ of

radius $\frac{2}{3} R$ and $\frac{1}{3} R$ have $12 \mu C$ and $-3 \mu C$

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 $S_{1}$ and $S_{2}$ are respectively :

1. $6 \mu \mathrm{C}$ and $3 \mu \mathrm{C}$

2. $+4.5 \mu \mathrm{C}$ and $-4.5 \mu \mathrm{C}$

3. $3 \mu \mathrm{C}$ and $6 \mu \mathrm{C}$

4. $4.5 \mu \mathrm{C}$ on both

Correct Option: 1

Solution:

Now

$\mathrm{Q}_{1}+\mathrm{Q}_{2}=\mathrm{Q}_{1}^{\prime}+\mathrm{Q}_{2}^{\prime}=12 \mu \mathrm{C}-3 \mu \mathrm{C}=9 \mu \mathrm{C}$

$\& \mathrm{~V}_{1}=\mathrm{V}_{2} \Rightarrow \frac{\mathrm{KQ}_{1}^{\prime}}{\frac{2 \mathrm{R}}{3}}=\frac{\mathrm{KQ}_{2}^{\prime}}{\frac{\mathrm{R}}{3}}$

$\mathrm{Q}_{1}^{\prime}=2 \mathrm{Q}_{2}^{\prime} \Rightarrow 2 \mathrm{Q}_{2}^{\prime}+\mathrm{Q}_{2}^{\prime}=9 \mu \mathrm{C}$

$\Rightarrow Q_{2}^{\prime}=3 \mu C$

$\& Q_{1}^{\prime}=6 \mu \mathrm{C}$