This problem obtains a general and important result about electric fields in conductors.Consider a solid metal sphere with charge Q and radius R. Imagine we've let the sphere sitafter charging

it, so that it's at equilibrium. This means that there are no net forces on the charges within the sphere. Can the charge Q be distributed uniformly throughout the volume of the sphere? Hint: imagine that the charge is made up of excess electrons, which is the case if Q is negative.Remember that charge can move within the volume of the conductor, and like-sign charges repel.How can the electrons get as far away from each other as possible? A similar argument applies when Q is positive. With this in mind, what is the electric field at a distance r < R from the center of the sphere,i.e. inside the sphere? Use Gauss's law: this one is easy once you see it!