# Electrostatic Self-energy of an arbitrary spherically symmetric charge density

1. Oct 11, 2007

### harshey

1. The problem statement, all variables and given/known data

Find an expression for the electrostatic self-energy of an arbitrary spherically symmetric charge density distribution p(r). You may not assume that p(r) represents any point charge, or that it is constant, or that it is piecewise constant, or that it does or does not cut off at any finite radius r. your expression must cover all possibilities. your expression may include an integral or integrals which cannot be evaluated without knowing the specific form of p(r).

2. Relevant equations

3. The attempt at a solution

I had no idea how to start this problem because i couldn't figure out what my professor meant by electrostatic self-energy of an arbitrary spherically symmetric charge density distribution.

Does anyone know a professor by the name is Ian Redmount?

2. Oct 12, 2007

### Meir Achuz

1. Find E(r) by using Gauss's law.
2. Integrate E to find$$\phi(r)$$.
3. $$U=(1/2)\int\rho\phi d^3 r$$ in Gasussian units.
This gives U as a triple integral integral involving rho twice.
What course is this and what is the text/

Last edited: Oct 12, 2007
3. Oct 12, 2007

### harshey

The course is Engineering Physics II at Saint Louis University in St. Louis MO.
The text is "Physics" Volume 2 by Halliday, Resnick and Krane.
Our professor doesn't use the text though, he teaches from his own notes which I believe are a few millennium old.

Thanks for the help I'll work on it right now and see if I can do exactly what you suggested but I may have more questions on the method but Thank You, I really appreciate it.

4. Oct 14, 2007

### harshey

Is the electrostatic self-energy the potential? What is phi in your equation? Sorry, I am confused in how you derived that equation.

5. Oct 15, 2007

### scienceleigh

phi is flux. that's about all I know. I have the same original question too. It would be nice if he wrote the questions in English instead of science speak that only interested physics majors understand.

Here's a link to gauss's law that breaks the equation down. It helps a little bit.

http://teacher.pas.rochester.edu/phy122/Lecture_Notes/Chapter24/Chapter24.html

6. Oct 16, 2007

### clem

The phi in my equation is the potential, given by integrating E.dr.
The electrostatic self-energy of a point charge is U= q*phi.
For charged sphere, it is given by my third equation.
I think that, on a Haliday and Resnick level,
there are too many simple things not given in the text to understand a problem on this level.