Electromagnetism II - 2024 entry

This is the second electromagnetism module taken by Physics students. It builds on PHY2021 (Electromagnetism I) and covers fundamental physics that students are capable of directly observing. The early part of the module provides a brief recap and reinforces the difficult material treated at the end of PHY2021. The Maxwell equations are stated and manipulated to obtain the wave equation, and the form of the solutions discussed. The dielectric and magnetic properties of solids are then introduced, with emphasis on the frequency dependence of their real and imaginary components, and the consequences for wave propagation. Wave propagation at interfaces between dissimilar materials is considered, leading to derivation of Fresnel reflection and transmission coefficients. The need to guide electromagnetic waves of different frequency is discussed, and guiding by transmission lines, waveguides and optical fibres is introduced. Finally the electromagnetic fields generated by charges moving with uniform or oscillatory velocity are discussed. A number of interesting physical phenomena are considered that are important in a wide variety of areas and in many key technologies. This is a core subject for Physics programmes and is supported by Stage 3 tutorials and problems classes.

1. Maxwell's equations for the electromagnetic field.
2. Scalar and vector potentials.
3. The equation of continuity.
4. The wave equation and wave solutions to Maxwell equations.
5. Linear, circular and elliptical polarization states of a wave.
6. Energy of a wave and the Poynting theorem.
7. The electromagnetic stress tensor and the momentum of an electromagnetic field.
8. Gauge invariance and Gauge fixing. The Weyl, Lorenz and Coulomb gauges.
9. Covariance of Maxwell equations and Lorentz transforms
10. Field generated by a moving charge. The Liénard-Wiechert potentials.
11. Larmor formula

1. Polarization of dielectric materials. Multipole expansion.
2. Electric susceptibility and the displacement field.
3. Clausius-Mossotti relation.
4. Boundary conditions for the electric and the displacement fields.
5. Magnetic dipoles and magnetization.
6. Magnetic susceptibility and the magnetic field.
7. Boundary conditions for the magnetic induction and the magnetic fields.
8. Larmor precession.
9. Paramagnetism and Curie law.
10. Ferromagnetism, spontaneous magnetization, and magnetic hysteresis.

1. Waves in non-conductive materials.
2. Waves in conductive materials and the skin effect.
3. Dispersive media and the group velocity.
4. Fresnel coefficients and their consequences (Snell's law, Brewster angle, total internal reflection).
5. Reflection and transmission from a conductive material.
6. Transmission lines and impedance.
7. The telegrapher's equation.
8. The rectangular waveguide. TE and TM modes of a waveguide.
9. Optical fibres.

1. Metals as plasmas, and the plasma frequency.
2. Plasma oscillations and plasmons.
3. Surface plasma polaritons.
4. Anisotropic media and the susceptibility tensor.
5. Biaxial and uniaxial media. Waveplates.
6. Double refraction.
7. Nonlinear media and the nonlinear polarization.
8. Nonlinear susceptibility.
9. Phase matching.
10. Wave diffraction. The Fresnel (paraxial) approximation and the Fraunhofer (far field) approximation.

Core text:

• Griffiths D.J. (2014), Introduction to Electrodynamics (4^th edition), Pearson Education, ISBN 978-0-321-85656-2 (UL: 537.6 GRI)

Supplementary texts:

• Garg A. (2012), Classical Electromagnetism in a Nutshell, Princeton University Press, ISBN 978-0-691-13018-7 (UL: 537 GAR)
• Kittel C. (2005), Introduction to Solid State Physics (8^th edition), Wiley, ISBN 978-0-471-41526-8 (UL: 530.41 KIT)
• Reitz J.R., Milford F.J. and Christy R.W. (1993), Foundations of Electromagnetic Theory (4^th edition), Addison-Wesley, ISBN 0-201-52624-7 (UL: 530.141 REI)

Reading list for this module: