Chapter 22 introduced the key idea that charged particles interact via the electric field. In this chapter you will learn how to calculate the electric field of a set of charges. We will start with discrete point charges, then move on to calculating the electric field of a continuous distribution of charge. The latter will let you practice the mathematical skills you’ve been learning in calculus. Only at the end of the chapter will we look at what happens to charges that find themselves in an electric field.

The electric fields used in science and engineering are often caused by fairly complex distributions of charge. Sometimes these fields require exact calculations, but much of the time we can understand the physics by using simplified models of the electric field. A model, you’ll recall, is a highly simplified picture of reality, one that captures the essence of what we want to study without unnecessary complications.

Four common electric field models are the basis for understanding a wide variety of electric phenomena. We present them here together as a reference; the first half of this chapter will then be devoted to justifying and explaining these results.