In this module, you will consolidate your knowledge of the integral form of Maxwell’s equations and discover their differential form appropriate for a vector calculus-based treatment of the fundamental aspects of electricity and magnetism. Numerical and graphical examples will emphasise the advantages of the vector calculus approach. You will learn to use coordinate systems that exploit the underlying natural symmetries of Gaussian surfaces and Amperian loops.

Topics include:

Gauss’s law

Gauss’s law for non-uniform charge distributions

Potential theory; work and energy in electrostatics.

Boundary conditions with conductors and insulators

Laplace’s equation; Poisson’s equation and interpretation of solutions; method of images

Polarisation and dielectric materials

Maxwell’s modification of Ampere’s law: justification for introducing the displacement current

The Lorentz force law

Gauss’s law for magnetic fields

Magnetic vector potential

Magnetisation; the H field

Linear and nonlinear media

Electromotive force

Faraday’s law

Maxwell’s equations with boundary conditions and derivation of the wave equation.