Two concentric conducting spherical shells have radii a and b , where b > a . Initially, the inner shell is given a charge Q and the outer shell is uncharged. If the two shells are then connected by a thin conducting wire, the final charge on the inner shell will be:

Step-by-step solution

Let the final charge on the inner shell be q_ in and on the outer shell be q_ out . The potential of the inner shell is the sum of the potentials due to its own charge and the charge on the outer shell: V_ in = k q_ in a + k q_ out b The potential of the outer shell is: V_ out = k q_ in b + k q_ out b When the shells are connected by a conducting wire, their potentials become equal ( V_ in = V_ out ): k q_ in a + k q_ out b = k q_ in b + k q_ out b k q_ in a = k q_ in b k q_ in ( 1 a - 1 b ) = 0 Since b > a , the t