l. Calculating the electric field for a spherically symmetric charge distribution Suppose we have an electron bunch that has spherical symmetry so that the charge density profile is only a function of r: p(r) = q ne (r), where q = e is the electron charge and n9 is the number density of the electrons. There is no neutralizing ion background, so the Coulomb force will ca use the bunch to expand. We will be comparing two radial profiles for the charge density to see whether they will maintain their shape during the expansion' (In the astrophysical example, the gas cloud would be collapsing since the force is attractive.) In this step, calculate the radial dependence of the electric field for two cases: - constant charge density pin up to a radius a, and - a Gaussian density profile p(r) = p0 e'/\"Z' You can use Gauss law; Compare the two fields by plotting for the same value of at We're just looking at the shape, so you can set p0 : l and a : 1 for the plot