In a certain region, a charge distribution exists that is spherically symmetric but nonuniform. That is, the volume charge density p(r) depends on the distance r from the center of the distribution but not on the spherical polar angles θ and Ф. The electric potential V(r) due to this charge distribution is


Where P0 is a constant having units of C/m3 and a is a constant having units of meters. (a) Derive expressions for E for the regions r ≤ a and r ≥ a. Explain why E has only a radial component.
(b) Derive an expression for p(r) in each of the two regions r ≤ a and r ≥ a.
(c) Show that the net charge contained in the volume of a sphere of radius greater than or equal to a is zero is this result consistent with the electric field for r > a that you calculated in part (a)?

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