We consider two widely separated conducting spheres, 1 and 2, the second having twice the diameter of the first. The smaller sphere initially has a positive charge q and the larger one is initially uncharged. The spheres are connected with a long thin wire. (a) We have to answer how the final potentials and are related. (b) We have to find the final charges and on the spheres in terms of q.

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It is given that the conducting sphere, 1, has initially charge q. The conducting sphere, 2, is initially uncharged. Let R be the radius of the sphere 1. The radius of the sphere 2 is .

After the conducting spheres have been connected with a long thin wire, there will be transfer of charge from 1 to 2 till the two become equipotential. Let the distributed charge on the conducting spheres when the two are equipotential be and . We have the condition

Therefore,