Two isolated conducting spheres S₁ and S₂ of radius $\frac{2}{3} R$ and $\frac{1}{3} R$ have $12 μC$ and $- 3 μC$ 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 S₁and S₂are respectively:

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$+ 4 .5 μC and - 4 .5 μC$

$3 μC and 6 μC$

$4 .5 μC on both$

$6 μC and 3 μC$

answer is A.

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Detailed Solution

Now $Q_{1} + Q_{2} = Q_{1}^{'} + Q_{2}^{'} = 12 μC - 3 μC = 9 μC$
$\begin{array}{l} & V_{1} = V_{2} \Rightarrow \frac{{KQ}_{1}^{'}}{\frac{2 R}{3}} = \frac{{KQ}_{2}^{'}}{\frac{R}{3}} \\ Q_{1}^{'} = 2 Q_{2}^{'} \Rightarrow 2 Q_{2}^{'} + Q_{2}^{'} = 9 μC \\ \Rightarrow Q_{2}^{'} = 3 μC \\ & Q_{1}^{'} = 6 μC \end{array}$