Introduction

Plan of the lectures for 2024

• Fields and potentials (Lectures 1-4): Maxwell's equations, boundary conditions, Laplace and Poisson equations, Laplace equation in spherical polars and cylindrical coordinates, multipole expansion
• Electric polarization (Lectures 5-6): Bound charges, polarization P, the electric displacement D, linear dielectrics, boundary conditions
• Magnetization (Lectures 7-9): Field from a current loop, magnetizable materials, diamagnetism, paramagnetism, ferromagnetism, hysteresis loops
• Electromagnetic waves in materials (Lectures 10-17): Displacement currents, Maxwell's equations in insulating dielectrics and in conductors, Poynting vector, radiation pressure, refraction, reflection, Fresnel equations, Brewster angle, plasmas, dispersion
• Confined electromagnetic waves (Lectures 17-19): Transmission lines, waveguides
• Signals and noise (Lectures 20-22): Fourier transforms of signals, sampling, Johnson noise, shot noise
• Special relativity and electromagnetism (Lectures 23): Lorentz transformation of E and B fields
• Examples and summary (Lecture 24)

Synopsis

Electromagnetic waves in free space. Derivation of expressions for the energy density and energy flux (Poynting vector) in an electromagnetic field. Radiation pressure. Magnetic vector potential. [Non-examinable: The change of E and B fields under Lorentz transformations in simple cases.] Dielectric media, polarisation density and the electric displacement D. Dielectric permittivity and susceptibility. Boundary conditions on E and D at an interface between two dielectrics. Magnetic media, magnetisation density and the magnetic field strength H. Magnetic permeability and susceptibility; properties of magnetic materials as represented by hysteresis curves. Boundary conditions on B and H at an interface between two magnetic media. Maxwell's equations in the presence of dielectric and magnetic media. Electromagnetic wave equation in dielectrics: refractive index and impedance of the medium. Reflection and transmission of light at a plane interface between two dielectric media. Brewster angle. Total internal reflection . [Non-examinable: Fresnel equations] The electromagnetic wave equation in a conductor: skin depth. Electromagnetic waves in a plasma; the plasma frequency. Dispersion and absorption of electromagnetic waves, treated in terms of the response of a damped classical harmonic oscillator. Treatment of electrostatic problems by solution of Poisson's equation using separation of variables in Cartesian, cylindrical or spherical coordinate systems. Theory of a loss-free transmission line: characteristic impedance and wave speed. Reflection and transmission of signals at connections between transmission lines and at loads; impedance matching using a quarter-wavelength transmission line. Fourier transform of signals (digital). Nyquist theorem. Interpolation and signal reconstruction. Noise (Johnson noise, shot noise, 1/f noise, digitization noise, interference noise).