Y2 Electromagnetism 2 (2023/24)

School of Physics and Astronomy ♦ University of Birmingham

Prof Evgueni Goudzovski

• Laws of electrostatics and magnetostatics in free space, in the integral form
• Lorentz force and relativity

• Definitions of gradient, divergence and curl
• Del and Laplace operators
• Useful theorems of vector calculus
• Laws of electrostatics and magnetostatics in the differential form

• Electric dipole moment; electric dipoles
• Dipole potential and electric field
• Dipoles in uniform and non-uniform external fields

• Ideal conductors in the electrostatic field
• Laplace and Poisson equations of electrostatics
• General problem of electrostatics; the uniqueness theorem
• The method of image charges

• Poisson equations of magnetostatics
• Magnetic dipoles
• Qualitative discussion of induced currents
• Faraday's law of electromagnetic induction
• Electromotive force in a loop of wire

• The continuity equation
• Modification of Ampere's law for non-steady currents
• The displacement current
• Maxwell's equations of electrodynamics in free space

• Polarisation of dielectric materials
• Polarisation charges and polarisation currents
• LIH materials; electric susceptibility
• Susceptibility for gaseous dielectrics

• 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

• Magnetic properties of atoms; the Bohr magneton
• Magnetisation and magnetic susceptibility
• Microscopic theory of diamagnetism and paramagnetism

• Surface and volume magnetisation currents
• The auxiliary H field
• Maxwell-Ampere law for the H field
• Example: a permanent magnet

• Relative permeability of materials
• Boundary conditions for the B and H fields
• Energy density of the magnetic field
• Ferromagnetism; hysteresis
• Electromagnets

• Wave equations in free space
• General solutions to the wave equations
• Monochromatic plane wave solutions

• Properties of monochromatic plane waves in vacuum and dielectrics
• Wave impedance
• EM energy flux: the Poynting vector

• Energy flux in a monochromatic plane wave
• Linear, circular and elliptic polarisations
• Absorptive linear polarisers; Malus's law
• Circular polarisers: quarter-wave plates

• Classical thoery of dispersion
• Complex refractive index
• Propagation and absorption of waves in dielectrics

• Boundary conditions for monochromatic waves
• Reflection and refraction
• Critical angle; total internal reflection
• Evanescent fields

• 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

• Ohm's law; conductivity in the low-frequency regime
• Wave number in conductors
• Definition of good conductors
• Refractive index in good conductors

• Wave attenuation in good conductors
• Wave impedance in good conductors
• Reflection at vacuum/good conductor boundary
• Skin effect

• Plasma oscillations, plasma frequency
• Refractive index of plasma
• Dispersion relation in plasma
• Properties of EM waves in plasma

• Motion in uniform electric and magnetic fields
• Cyclotron frequency and radius
• Principles of mass spectrometry
• Thomson's parabola spectrometer
• Electrostatic lenses (non-uniform field)

• Transmission lines
• Wave propagation in a parallel wire line
• Wave propagation in a rectangular waveguide