• To build on first and second year modules on electricity, magnetism and waves by understanding a range of electromagnetic phenomena in terms of Maxwell''s equations.
• To understand the properties of solutions to the wave equation for electromagnetic fields in free space, in matter (non-dispersive and dispersive dielectrics, and conductors).
• To understand the behaviour of electromagnetic waves at boundaries.
  
• To understand the behaviour of electromagnetic waves in cavities, waveguides and transmission lines.
• To understand the properties of electric dipole radiation.
• To introduce an explicity covariant formulation of electromagnetism in special relativity.
• To further develop students'' problem-solving and analytic skills.

Students should have an understanding of the properties of solutions to the wave equation for electromagnetic fields in free space and in matter (non-dispersive and dispersive dielectrics, and conductors).

Students should have an understanding of the behaviour of electromagnetic waves at boundaries.

Students should have an understanding of the behaviour of electromagnetic waves in cavities, waveguides and transmission lines.

Students should have an understanding of the properties of electric dipole radiation.

Students should have the ability to explain an explicity covariant formulation of electromagnetism in special relativity.

1. Introduction: Maxwell''s equations.
• Maxwell''s equations and their physical significance.
• Continuity equation and conservation of charge.
• Poynting''s theorem: energy density and energy flux in an electromagnetic field.
2. Electromagnetic waves in dielectric media.
• Non-dispersive media: derivation of the wave equation.
• Dispersive media: atomic model, normal and anomalous dispersion.
3. Electromagnetic waves in conducting media.
• Derivation of the wave equation in a conductor.
• Properties of the solution to the wave equation in the limits of low conductivity and high conductivity.
• Attenuation and skin depth.
• Drude model: frequency-dependent conductivity.
4. Waves incident on a boundary between two media.
• Boundary conditions for electromagnetic fields.
• Derivation of Fresnel''s equati ons.
• Physical consequences of Fresnel''s equations: total internal reflection and critical angle; polarisation by reflection and Brewster angle.
5. Electromagnetic cavities and waveguides.
• Solutions to the wave equations with perfectly-reflecting boundaries.
• Resonant cavities.
• Waveguides: TE and TM modes; phase and group velocity; cut-off frequency.
6. Transmission lines.
• LC model of a transmission line.
• Solution to the wave equation for current and voltage.
• Phase velocity and characteristic impedance in an infinite transmission line.
• Termination of a transmission line.  Impedance matching.  Voltage standing wave ratio.
• Lossy transmission lines: dispersion.
• Calculation of characteristic impedance in parallel wire and coaxial transmission lines.
  
7. Electromagnetic potentials.
• Relationship between potentials and fields.
• Gauge inva riance: Coulomb gauge and Lorenz gauge.
• Wave equations for the potentials with source terms.
• Solutions to the wave equations for the potentials.
8. Sources of electromagnetic radiation.
• Hertzian dipole: solution for vector potential, and for electric and magnetic fields.
• Properties of dipole radiation: spatial intensity, polarisation.
• Radiation resistance.
• Half-wave antenna.
9. Electromagnetism and special relativity.
• Lorentz scalars, four-vectors and tensors.
• Lorentz transformation of potentials and fields.
• Explicitly covariant form of Maxwell''s equations.

Lecture -

Tutorial -