A conducting spherical shell has inner radius a and outer radius b. A point charge +Q sits at the centre, and a total charge -q is placed on the shell. How is the charge -q distributed on the shell's surfaces?

-Q on the inner surface, -q on the outer surface
-Q on the inner surface, (-q + Q) on the outer surface
+Q on the inner surface, (-q - Q) on the outer surface
the charge -q spreads uniformly through the whole shell

Correct answer: -Q on the inner surface, (-q + Q) on the outer surface

Solution

The central +Q induces -Q on the inner surface so the field inside the conductor is zero. Charge conservation on the shell: inner + outer = -q, so outer = -q - (-Q) = -q + Q.

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