Consider a small sphere (an actual sphere, not a Gaussian surface) of radius 0.1 m that is charged throughout its interior, but not uniformly so. The charge density (in C/m) is p= Br, where r is the distance from the center, and B-10 C/m' is a constant. Of course, for r greater than 0.1 m, the charge density is zero. radius = 0.1 m (a) What is the charge density at the center? Does it increase or decrease as we move toward the surface? (b) What is E at the center? How do you know? How does this compare to the E of a point charge? (c) Apply Gauss' Law to find E at r = 0.05 m. Your answer should be in N/C [Hint: the volume of a thin spherical shell is dV = 4xr dr. You can find E(r) for r inside the sphere and then evaluate at r=0.05 m. Also, &=8.85x10-12, C Nm ]