I have a HW problem for non-calculus based physics that I can't seem to figure out. Please help me if you can: Consider a sphere of radius R woth a uniform positive charge distribution (rho)=q/V. Using Gauss's law, prove (a) that the magnitude of the electric field outside the spherical volume is E=q/4(pi)(permittivity of free space)r^2= (rho) R^3 / 3 (permittivity of free space)r^2, (b) that the magnitude of the electric field insode the sphere at a distance r from the center is E=(rho)r/(permittivity), (c) compare the results of a and b when r=R. I have Gauss's law: E(4(pi)r^2=4(pi)koQ and that for r>R, E=ko Q/r^2 and i substituted in (rho)V for Q and 4/3 (pi)r^3 for V and simplified, but this did not prove part A. And for r<R, Q'=Q(r/R)^3 because the inner sphere encloses a volume 4/3 (pi)r^3 which is (r/R)^3 times the total volume. but this doesn't work out either. And how do i reconcile ko from coulomb with the permittivity?