Department of Physics and Astronomy
Arizona State University
Tempe, AZ U.S.A.
Electrodynamics has the reputation of being one of the harder subjects that a physicist must learn. In reality, it is a much easier subject than quantum mechanics. For example to describe the electronic structure of a Neon atom with just 10 electrons already requires solving a 30 dimensional Schrödinger equation. Text book problems in quantum mechanics often hide this chasm of solving differential equations in a huge number of dimensions, by only addressing single particle problems.
Happily, in electrodynamics, we are safely ensconced in three spatial and one time dimension, and this makes both analytical and numerical techniques much more tractable. It is partly because we have many tools available that the subject can be daunting.
Numerical methods can be used to solve for situations and geometries that are difficult analytically. Visualization techniques can be used to view the fields and sources and get a better physical feeling for how the solution arises.
To begin let's see how to calculate some of the basic operations of vector calculus. I will assume that we are working in cartesian coordinates. Generally, cartesian coordinates are the simplest for numerical work. Most interesting problems do not have the symmetries necessary to exploit spherical or cylindrical coordinates and these coordinate systems have the major disadvantage of having unit vectors that point in different directions depending on the position.