# Homework Help: Spherically Symmetric Charge Distribution

1. Apr 16, 2012

### steelclam

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

Consider a spherically symmetric charge distribution $$\rho = \rho (r)$$

2. Relevant equations

By dividing the charge distribution into spherical shells, find the potential $$\phi$$ and the electric field strength $$\bf{E}$$ in terms of $$\rho (r)$$

3. The attempt at a solution

The given solution is

$$\phi (r) = \frac{4 \pi}{r} \int_0^r \rho (r\prime) {r \prime}^2 dr \prime + 4\pi \int_r^\infty \rho (r\prime ) r \prime dr \prime$$
I just can't understand the separation in two integrals, I think it is not rigorous...by the way the book (Problems in Electrodynamics, Batygin and Toptygin) uses non-SI units.