Consider a sphere of radius a with a uniform charge distribution over its volume, and a total charge of qo.

Consider a sphere of radius a with a uniform charge distribution over its volume, and a total charge of qo. Use Gauss's Law to calculate the electric field outside the sphere, and then inside the sphere. Solve the general problem in r, recognizing that the problem has spherical symmetry. Draw a graph of the electric field strength as a function of r, noting where the surface of the sphere is (a). Some hints: the surface area of a sphere of radius r is 4πr2 , and if the sphere is charged uniformly throughout the volume, then the charge density is simply the charge per unit volume, or the total charge divided by the total volume. This idea will enable you to calculate not only the charge density, but by using it backwards, the charge inside a smaller Gaussian sphere with the same charge density. Finally, note that while this looks a lot the first Gauss's law problem we did, the difference is in the charge being evenly distributed throughout the volume of the sphere and not on the surface. Thus, you might find the same field strength outside the sphere, but should expect it to be different inside the sphere