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## Homework Statement

A point charge +Q is placed at the centre of an isolated conducting shell of radius R. Find the electrostatic potential energy stored outside the spherical shell if the shell also contains a charge +Q distributed uniformly over it.

## Homework Equations

[/B]

E=kQ/r

^{2}.

dU/dV=(1/2)ε

_{o}E

^{2}, where V is volume, U is potential energy.

## The Attempt at a Solution

The charge +Q inside the conductor will induce -Q charge on the inside surface, which further leads to +2Q charge on the outer surface of the shell. Therefore E=2kQ/r

^{2}.

My question is, why have we used the formula dU/dV=(1/2)ε

_{o}E

^{2}. How did we derive it? Isn't it equal to the energy of a charged capacitor.

Sorry if this a bad question, I just want to know how did we derive this formula.

Thanks.