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



Where P0 = 3Q/πR3 is a positive constant.
(a) Show that the total charge contained in the charge distribution is Q.
(b) Show that the electric field in the region r ≥ R is identical to that produced by a point charge Q at r = 0.
(c) Obtain an expression for the electric field in the region 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.

p(r) = Po (1- r|R) for rsR for rSR Po (1- r|R) for r> R p(r) = 0