(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Calculate the work that must be done to charge a spherical shell of radius [tex]R[/tex] to a total charge [tex]Q[/tex].

No diagram was provided.

(Another user posted the same question at https://www.physicsforums.com/showthread.php?t=109489, but there was no solution and the thread is ancient.)

2. Relevant equations

I'm not sure what equations are needed, so I'm just guessing here.

[tex]U = k_e\frac{q_1q_2}{r_{12}}[/tex]

[tex]W = -\Delta U[/tex]

[tex]V = k_e\frac{q}{r}[/tex] for a sphere

3. The attempt at a solution

I know the answer is [tex]\frac{k_eQ^2}{2R}[/tex] from the back of the book, but I don't know how to get it. I've reread the chapter and all the examples, but I can't find anything talking about energy with just one object. Everything deals with pairs or movement in a field. I thought about making up an identical sphere with charge [tex]-Q[/tex] next to the existing one and finding the change in potential energy. This gets me the right answer, but I doubt that this is a correct process.

Any help would be appreciated.

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# Homework Help: Work needed to charge a sphere

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