1.2 The electromagnetic model

There are two ways to build a physical theory. The inductive way follows the historical development: one starts from many separate experimental observations and gradually generalises them. The deductive way, which is the one adopted here (and in the textbook of the course), starts from a small number of carefully chosen basic laws, the fundamental postulates, and derives everything else from them by mathematics.

Following this approach, the theory is constructed in three steps.

1. Define the basic quantities: the sources and the fields (Section 1.3).
2. Specify the rules of operation: the mathematics with which the quantities are handled. Because the fields are vectors that vary from point to point, this is vector algebra and vector calculus: the gradient, the divergence and the curl, and the integral theorems of Gauss and Stokes (Chapter 2).
3. Postulate the fundamental relations: a few experimental laws, written in terms of the basic quantities. In electrostatics the single experimental input is Coulomb's law for the force between two point charges (Section 3.1). From it, with the superposition principle, the field of any charge distribution, Gauss's law (Section 3.2), the electrostatic potential and the equations of Laplace and Poisson (Section 3.3), and the behaviour of fields in dielectrics and around conductors (Section 3.4) are all derived.

In class these derivations are done step by step on the board. In these notes they are written out in full, so that each result can be traced back to the few laws that were assumed.