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## Homework Statement

A point charge q is at the center of a spherical conducting shell of inner radius a and outer radius b. How much work would it take to remove the charge out to infinity?

## Homework Equations

Potential, W = 1/2qV

## The Attempt at a Solution

I am going at this in layers, but getting the wrong result.

The work to bring the point charge to the center is zero (with nothing else in place yet). The work to bring in the -q on the inner radius a is W = -(1/2)qV.

The work to bring in the outer radius of charge q is W = (1/2)(q)[V from a + V from center point charge). The separation distance from a is (b-a) and just a from the center. Then what should I be doing with this? Should I add the work to bring in the -q to a and +q to b? When I do so, I get zero! :0 please help!