Chapter 22, Problem 22.56P

CALC A nonuniform, but spherically symmetric, distribution of charge has a charge density ρ(r) given as follows:

$\begin{array}{l}\rho (\text{r})={\rho }_0\left(1-\frac{4\text{r}}{3\text{R}}\right)for\text{ r }\le \text{ R}\\ \rho (\text{r})=0for\text{ r }\ge \text{ R}\end{array}$

where ρ₀ is a positive constant. (a) Find the total charge contained in the charge distribution. Obtain an expression for the electric field in the region (b) r ≥ R; (c) r ≤ R. (d) Graph the electric-field magnitude E as a function of r. (e) Find the value of r at which the electric field is maximum, and find the value of that maximum field.