Introduction

Armed with the necessary tools of vector operations and vector calculus, we are now ready to explore electromagnetic field theory. In this chapter, we study static electric fields (electrostatics), due to charges at rest. A charge can either be concentrated at a point or distributed in some fashion. In any case, the charge is assumed to be constant in time.

We begin our discussion by stating Coulomb's law of electrostatic force between two point charges fixed in space. We define the electric field intensity as the force per unit charge. We then want to establish that

1. The electric field intensity is irrotational or conservative, and

2. The work done in moving a charge from one point to another in an electrostatic field is independent of the path taken and depends only upon the endpoints of the path.

We will express the electric field intensity in terms of electric potential and deduce an expression for the energy required to move a charge from one location to another in an electrostatic field.

We will also explore the influence of the medium on electrostatic fields and define bound charge densities; examine several methods (Gauss's law, Poisson's and Laplace's equations, method of images) of solving electrostatic field problems; and develop the concept of capacitance and obtain an equation for the energy stored in a capacitor.