Two isolated conducting spheres


Two isolated conducting spheres $S_{1}$ and $S_{2}$ of radius $\frac{2}{3} R$ and $\frac{1}{3} R$ have $12 \mu \mathrm{C}$ and $-3 \mu \mathrm{C}$ 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. (1) $4.5 \mu \mathrm{C}$ on both

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

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

  4. (4) $6 \mu \mathrm{C}$ and $3 \mu \mathrm{C}$

Correct Option: 1


(1) Total charge $Q_{1}+Q_{2}=Q_{1}^{\prime}+Q_{2}^{\prime}$

$=12 \mu C-3 \mu C=9 \mu C$

Two isolated conducting sphres $S_{1}$ and $S_{2}$ are now connected by a conducting wire.

$\therefore V_{1}=V_{2}=\frac{K Q_{1}^{\prime}}{\frac{2}{3} R}=\frac{K Q_{2}^{\prime}}{\frac{R}{3}}=12-3=9 \mu \mathrm{C}$

$Q_{1}^{\prime}=2 Q_{2}^{\prime} \Rightarrow 2 Q_{2}^{\prime}+Q_{2}^{\prime}=9 \mu C$

$\therefore Q_{1}^{\prime}=6 \mu C$ and $Q_{2}^{\prime}=3 \mu C$

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