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Two identical uncharged metal spheres (1 and 2), each of radius r, are placed a distance d apart with d >> r. A third sphere of the same radius carrying charge q is brought into contact with sphere 1 and then taken far away. Sphere 2 is then connected to earth. What charge remains on the earthed sphere 2?

1. -qr/2d
2. q
3. -q
4. 0

Correct answer: -qr/2d

Solution

Contact shares charge equally, so sphere 1 gets q/2. The potential at sphere 2 due to sphere 1 (distance d) plus the potential from sphere 2's own charge q2 (radius r) must vanish on earthing: kq2/r + k(q/2)/d = 0, giving q2 = -qr/(2d).

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