(Course description last updated for academic year 2021-22).
Prerequisites

It helps to have studied Electromagnetic Fields in Part IA Physics, but it is not vital.

Learning Outcomes and Assessment

The electromagnetism course further develops the idea of electric and magnetic fields introduced in Part IA. The goal of the course is to arrive at the full set of Maxwell's equations that provide a complete description of classical electromagnetism, building them didactically by introducing each of the term, examining the experimental evidence, and studying the theoretical implications. The course starts with electrostatics and magnetostatics and then introduces dielectric and magnetic media. Finally, the Faraday displacement current is introduced and dynamic phenomena are studied, starting from simple LC-circuits, over wave propagation in free space, as well as in insulating and conducting media, and on transmission lines and in waveguides.

Synopsis

Introduction: Electromagnetism in physics, and the role of Maxwell’s equations.

Electrostatic fields: Electrostatic force, electric field, potential, grad, curl, line integrals, Stokes’s theorem, conservative fields, electric monopoles, electric dipoles, field of a dipole, couple and force on a dipole, energy of a dipole, multipole expansions, electric flux, divergence, divergence theorem, charge conservation, Gauss’s law, solutions for simple geometries, Laplace’s and Poisson’s equations, boundary conditions and uniqueness, conducting sphere in uniform E field, method of images, line charge near conducting cylinder, capacitance, capacitance of parallel cylinders, energy stored in electric field, force and virtual work, force on charged conductor.

Electrostatic fields in dielectric materials: Isotropic dielectrics, polarisation, polarisation charge density, Gauss’s law for dielectric materials, permittivity and susceptibility, properties of D and E, boundary conditions at dielectric surfaces, field lines at boundaries, relationship between E and P, thin slab in field, dielectric sphere in field, energy density in dielectrics, general properties of dielectrics.

Magnetostatic fields: Force on and between current elements, magnetic flux, the ampere, ∇.B=0, magnetic dipoles, force and couple on a dipole, energy, magnetic scalar potential, solid angle of a loop, Ampère’s law, magnetic vector potential. Ohm’s law as JE.

Magnetostatic fields in magnetic materials: magnetisation, existence of diamagnetism and paramagnetism, permeability and magnetic susceptibility, properties of B and H, boundary conditions at surfaces, methods for calculating B and H, magnetisable sphere in uniform field, electromagnets.

Time-varying electromagnetic fields: Faraday’s law, emf, electromagnetic induction, Faraday’s law for a circuit, interpretation of Faraday’s emf, self-inductance, inductance of long solenoid, coaxial cylinders, parallel cylinders, mutual inductance, transformers, magnetic energy density.

Electromagnetic waves: equation of continuity, displacement current, Maxwell's equations, electromagnetic waves, velocity of light, plane waves in isotropic media, energy density, Poynting's theorem, radiation pressure and momentum, insulating materials. Characteristic impedance, reflection and transmission at an angle, total internal reflection; plasmas and the plasma frequency, evanescent waves; conducting media, skin effect. Guided waves, transmission lines, characteristic impedance; coaxial, parallel-wire, strip transmission lines; power flow; terminated lines, matching, reflection and transmission coefficients, impedance of short-circuited lines, impedance matching, introduction to waveguides, TE modes, waveguide equation, cut-off frequency, characteristic impedance.

Summary of Maxwell’s equations:  Restatement of equations, physical interpretation, classes of solutions, and applications.

Course section:

Other Information

Staff
Dr Oleg BrandtLecturer