Y2 Electromagnetism 2 (2023/24)

School of Physics and Astronomy ♦ University of Birmingham

Prof Evgueni Goudzovski

Contact details: Physics West 212, email goudzovs@cern.ch.


This page contains the notes of the "Electromagnetism 2" lecture course offered to Year 2 students at the School of Physics and Astronomy, University of Birmingham in the spring semester of 2023/24. A set of non-assessed problems is also provided. Further materials are available to the students following the course at the University of Birmingham via Canvas/Panopto.

Familiarity with the "Electromagnetism 1" course and vector calculus is assumed.

Lecture notes

Summary Notes
1 Static electric and magnetic fields
  • Laws of electrostatics and magnetostatics in free space, in the integral form
  • Lorentz force and relativity
[pdf]
2 Revision of vector calculus
  • Definitions of gradient, divergence and curl
  • Del and Laplace operators
  • Useful theorems of vector calculus
  • Laws of electrostatics and magnetostatics in the differential form
[pdf]
3 Electric and magnetic dipoles
  • Electric dipole moment; electric dipoles
  • Dipole potential and electric field
  • Dipoles in uniform and non-uniform external fields
[pdf]
4 Ideal conductors; electrostatic problems
  • Ideal conductors in the electrostatic field
  • Laplace and Poisson equations of electrostatics
  • General problem of electrostatics; the uniqueness theorem
  • The method of image charges
[pdf]
5 Magnetostatics; electromagnetic induction
  • Poisson equations of magnetostatics
  • Magnetic dipoles
  • Qualitative discussion of induced currents
  • Faraday's law of electromagnetic induction
  • Electromotive force in a loop of wire
[pdf]
6 Maxwell's equations in free space
  • The continuity equation
  • Modification of Ampere's law for non-steady currents
  • The displacement current
  • Maxwell's equations of electrodynamics in free space
[pdf]
7 Dielectric materials
  • Polarisation of dielectric materials
  • Polarisation charges and polarisation currents
  • LIH materials; electric susceptibility
  • Susceptibility for gaseous dielectrics
[pdf]
8 Electric field in dielectric materials
  • The electric displacement field D; relative permittivity
  • Gauss's law for the D field
  • Boundary conditions for the E and D fields
  • E and D field lines at boundaries
  • Energy density of the electric field
[pdf]
9 Diamagnetism and paramagnetism
  • Magnetic properties of atoms; the Bohr magneton
  • Magnetisation and magnetic susceptibility
  • Microscopic theory of diamagnetism and paramagnetism
[pdf]
10 Magnetic field in materials (part 1)
  • Surface and volume magnetisation currents
  • The auxiliary H field
  • Maxwell-Ampere law for the H field
  • Example: a permanent magnet
[pdf]
11 Magnetic field in materials (part 2)
  • Relative permeability of materials
  • Boundary conditions for the B and H fields
  • Energy density of the magnetic field
  • Ferromagnetism; hysteresis
  • Electromagnets
[pdf]
12 Electromagnetic waves in free space
  • Wave equations in free space
  • General solutions to the wave equations
  • Monochromatic plane wave solutions
[pdf]
13 EM waves in dielectrics; Poynting vector
  • Properties of monochromatic plane waves in vacuum and dielectrics
  • Wave impedance
  • EM energy flux: the Poynting vector
[pdf]
14 Polarisation of plane waves
  • Energy flux in a monochromatic plane wave
  • Linear, circular and elliptic polarisations
  • Absorptive linear polarisers; Malus's law
  • Circular polarisers: quarter-wave plates
[pdf]
15 Dispersion of waves in dielectrics
  • Classical thoery of dispersion
  • Complex refractive index
  • Propagation and absorption of waves in dielectrics
[pdf]
16 EM waves at boundaries of dielectrics
  • Boundary conditions for monochromatic waves
  • Reflection and refraction
  • Critical angle; total internal reflection
  • Evanescent fields
[pdf]
17 The Fresnel equations
  • S and P polarisations of plane waves
  • Derivation of the Fresnel equations
  • Main properties of the Fresnel coefficients
  • Brewster's angle
  • Energy transport at boundary
[pdf]
18 Low-frequency EM waves in conductors
  • Ohm's law; conductivity in the low-frequency regime
  • Wave number in conductors
  • Definition of good conductors
  • Refractive index in good conductors
[pdf]
19 Low-frequency EM waves in good conductors
  • Wave attenuation in good conductors
  • Wave impedance in good conductors
  • Reflection at vacuum/good conductor boundary
  • Skin effect
[pdf]
20 EM waves in plasma
  • Plasma oscillations, plasma frequency
  • Refractive index of plasma
  • Dispersion relation in plasma
  • Properties of EM waves in plasma
[pdf]
21 Motion of charges in uniform fields
  • Motion in uniform electric and magnetic fields
  • Cyclotron frequency and radius
  • Principles of mass spectrometry
  • Thomson's parabola spectrometer
  • Electrostatic lenses (non-uniform field)
[pdf]
22 Transmission lines and waveguides
  • Transmission lines
  • Wave propagation in a parallel wire line
  • Wave propagation in a rectangular waveguide
[pdf]

Non-assessed problems

Reading list

Suggested textbooks, ordered from basic to advanced:

Prof E Goudzovski / goudzovs@cern.ch