PHYSICS 422 – ELECTROMAGNETIC THEORY

JANUARY 2005 F.I. COOPERSTOCK

References: “Mechanics and Electrodynamics”, L.D. Landau & E.M. Lifshitz

“The Classical Theory of Fields”, L.D. Landau & E.M. Lifshitz, Pergamon Press

“Electromagnetic Fields and Waves, P. Lorrain, D.R. Corson and F. Lorrain, 3^rd edition, Freeman

“Classical Electrodynamics”, J.D. Jackson, John Wiley & Sons

1. Fundamentals of Special Relativity

- Principle of Relativity

- Lorentz Transformation

- Lorentz contraction, time dilation

- Transformation of velocities

- Lorentz four-vectors

- Action principle (brief overview), connection to the Lagrangian

- Hamiltonian, energy, momentum, energy-momentum 4-vector

2. Electromagnetic Fields and Charged Particles

- Four-vector potential

- Lagrangian and Hamiltonian of a charged particle in a given electromagnetic field

- Motion of a charge in a given field, Lorentz force

- Electric, magnetic field intensities

- Rate of change of mechanical energy due to an electromagnetic field

- Gauge transformations, gauge invariance

- Constant and uniform electromagnetic fields, forms for potentials

- Motion of a charge in constant uniform electric and magnetic fields

- The Maxwell tensor of the electromagnetic field

- Transformation of electromagnetic fields

- Fundamental field invariants

3. The Maxwell Equations

- First pair of Maxwell equations, derivation

- Physical consequences, absence of magnetic monopoles, Faraday’s law of electromagnetic induction

- Experimental and mathematical reasons leading to the free-field Lagrangian

- Current four-vector

- Conservation of charge in differential form

- Second pair of Maxwell equations, description of derivation only

- Physical implications, Gauss flux law, circulation of magnetic field related to true and displacement currents

- Conservation of charge as a consequence of the Maxwell equations

Physics 422 – Syllabus, January 2001 – p. 2

- Energy density and energy flux for electromagnetic fields, the Poynting vector

- Conservation of total energy including fields

4. The Electrostatic Field

- Poisson, Laplace equations

- Field of a spherical point charge

- Solving Laplace equation in rectangular Cartesian coordinates

- Field between two grounded semi-infinite parallel electrodes terminated by a plane electrode maintained at fixed potential

- Laplace’s equation in spherical polar coordinates, Legendre polynomials

- Uncharged conducting sphere in a previously uniform electric field

- Surface charge density on a conducting sheet, relation to electric field

5. Field of a Uniformly Moving Charge

- Potentials, field intensities

- Angular distribution of intensity

- Force between two charges moving with constant velocity

6. Multipole Expansions for Fields

- Monopole, dipole, quadrupole potentials for the electric field

- Multipole moments, trace-free quadrupole tensor

- Potential for magnetostatic field

- Magnetic dipole moment

7. Electromagnetic Waves

- Gauge conditions leading to the wave equation

- Plane waves

- Orientation of electric and magnetic fields relative to direction of wave propagation

- Poynting vector for a plane wave, relation to energy density

- Monochromatic waves, the wave three-vector and wave four-vector

- The Doppler effect, general formula

- Transverse Doppler effect

8. Electromagnetic Radiation

- Connection of the fields to sources

- Lorentz gauge condition

- Retarded potentials, causality

- Field of an arbitrarily moving point charge (no derivation), description

- Wave zone radiation field

Physics 422 – Syllabus, January 2001 – p. 3

- Conditions on source size, velocity, wavelength

- Electric dipole radiation, intensity, angular distribution

- Electric quadrupole and magnetic dipole radiation (no derivation)

9. Radiation From Antennas

- Short-length centre-fed linear antenna, radiated power

- Centre-fed linear antenna, exact treatment

- Angular distribution of power radiated

- Half-wave and full-wave power distributions

- Radiation resistance

10. Scattering of Electromagnetic Waves

- Descriptive treatment

- Differential scattering cross-section, Thomson cross-section

- Descriptive treatment for atomic and molecular dipole oscillators

- Atmospheric effects

11. Electromagnetic Waves in Continuous Media

- Derivation of Maxwell equations in continuous media

- Dielectrics, polarization vector, electric displacement vector, permittivity

- Magnetic induction vector, permeability

- Wave equation in a non-conducting medium, wave propagation velocity

- Waves in conducting media, conductivity, Ohm’s law

- Constant uniform longitudinal magnetic field intensity, decay of longitudinal electric field intensity

- Complex wave vector

- Wave attenuation for poor conductors, frequency independence

- Wave attenuation for good conductors, frequency-dependent attenuation

- Magnetic field lagging the electric field, ratio of amplitudes, phase shift

- Skin depth

- Model for conductivity, equation of motion of charges with damping due to collisions

- Complex conductivity

- Transverse waves in a tenuous plasma

- Plasma frequency, relation to the index of refraction

- Penetration depth in a plasma