We apply Gauss's Law in integral form:
We take the closed surface to be a sphere of radius concentric with the sphere in the problem statement. Also, let be the charge density, which we know is a constant. Then by Gauss's Law, we have,
Thus, we see that the relationship between radius and electric field is a linear one, and so curve C must be correct. Hence the answer is (C). For , the electric field falls off like and is identical to the electric field produced by a point charge with charge .