In this unit, we consider charges, electric fields, and the electric potential in and around conductors. Electric charge can move freely through conductors such as metal objects. The human body and the Earth are also conductors. When charges move through metals, it is the negatively charged electrons that are mobile. Wood, plastic, stone, and glass are all insulators. Charges cannot move easily in these materials. Another word for insulators is "dielectrics." While no material is either a perfect insulator or a perfect conductor, most materials can be classified as one or the other. In insulators, charge can be placed arbitrarily. According to the definition of an insulator, the charges can’t move. On the other hand, in a conductor, charges are free to move. As a result, any excess charge must reside on the surface of the conductor. To understand why this is true, let us consider the electric field inside a conductor. Here is a metal rod containing many electric charges. This figure shows all the charges, not just the excess charges. If the conductor is electrically neutral, it will contain equal positive and negative charges in equal measure. To simplify things, let’s hide the positive charges, which can’t move. Keep in mind that a deficit of negative charge in part of the conductor will result in that part’s being positively charged. Next, impose an electric field in the conductor by fixing positive charges near one end. These fixed charges will result in the formation of an electric field that is directed away from them. The electric field will cause the negative charges to move toward the fixed positive charges. The negative charges will accumulate near the fixed positive charges, and the electric field will decrease. The charges will continue to move until no electric field remains. The mobile charges in a conductor move almost immediately to cancel any electric field there. In a steady state ­ which by definition has no moving charges ­ there can be no electric field inside a conductor. We are looking closely at part of the surface of a conductor that has reached a steady state. Suppose the electric field had a component along the surface. In the presence of this component, a component of the force on the charge directed along the surface would also be present, and this would accelerate the charge. F perpendicular is the component of the force perpendicular to the surface, and F parallel is the component parallel to it. Because these forces cannot be present in a steady state, the electric field must be exactly perpendicular to the surface everywhere. Recall that the electric field is related to a gradient in the electric potential. If there is no electric field inside a conductor, the electric potential, V, must be uniform. The surface of a conductor is an equipotential. As an analogy to the electric field and potential inside a conductor, consider the surface of a fluid. If the surface were not flat, gravity would eventually flatten the surface. An undisturbed fluid surface is flat. It is an equipotential surface with respect to gravity. Suppose we have two conductors, one charged and one uncharged. The surface of each is an equipotential. If we connect the two conductors with a conducting wire, the surfaces of the two conductors and the wire must be an equipotential. Charges must flow from the charged to the uncharged sphere.

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