In the previous page of notes, we showed that there must be some charges along the surface of a wire and they must be arranged in a gradient. We call these charges along the surface of the wire surface charges. The surface charges create an electric field in the wire, which then pushes electrons through the wire to create a current. In this page of notes, we will dig a little deeper into what a gradient of surface charges actually is and how we represent that gradient on a drawing.

A gradient is simply a change in the amount of something. For example, you may have seen a color gradient (like the one shown at the right), where you start with a single color that slowly fades to white. In this case, the color is what is changing, so we call it a “color gradient.” Similarly, when we talk about a surface charge gradient on a wire, this means that we are talking about a change in the amount of charge along the wire. The word change here is really important. It is not simply that there are a lot of charges on the surface of the wire. For a surface charge gradient to exist, there must be areas on the wire with a lot of positive charge, areas with less positive charge, areas with almost no charge, areas with less negative charge, and areas with a lot of negative charge.