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Q.

Two isolated conducting spheres S1 and S2  of radius 23R  and  13R 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  S1 and  S2 are respectively :

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a

6  μC     and   3  μC

b

4.5  μC     on   both

c

+4.5  μC     and     −4.5   μC

d

3  μC     and     6   μC

answer is A.

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Detailed Solution

After connected, Both spheres are at same potential.q1C1=q2C2Capacitance of sphere, C∝RTotal charge=Q=q1+q2Let say q1 =q, then q2= Q-q1=12-3-q⇒q2=(12-3)-q1⇒q=18-2q⇒q=6Hence, q1 =q =6μCq2= Q-q1=12-3-q=9-6=3μC
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