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Two thin concentric conducting shells have radii R and 3R. The outer shell (radius 3R) carries charge +Q and the inner shell (radius R) is initially neutral. The inner shell is then connected to earth through a switch S. What charge does the inner shell acquire?

1. -Q/3
2. +Q/3
3. +Q/2
4. -Q/2

Correct answer: -Q/3

Solution

Let the inner shell acquire charge q after earthing. The potential at the inner shell (radius R) is the sum of its own potential k q/R and that due to the outer shell k Q/(3R) (uniform inside the outer shell). Earthing sets this to zero: q/R + Q/(3R) = 0, giving q = -Q/3.

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