** **

**Introduction:** Course overview, electromagnetic units

**Foundations of special relativity:** Spacetime intervals**,** proper time**,** the Lorentz transformation**,** transformation of velocities**,** vectors and tensors in spacetime**,** four-velocity and four-acceleration

**Relativistic dynamics:** The principle of least action**,** momentum and energy**,** Lorentz invariance of phase-space density**,** particle collisions**,** angular momentum

**Charges in electromagnetic fields:** Action, Lagrangian, and Hamiltonian**,** equations of motion**,** gauge invariance**,** motion in constant uniform electromagnetic fields**,** motion in slowly-varying electromagnetic fields**,** electromagnetic field tensor

**Electromagnetic field equations:** Source-free Maxwell equations**,** charge and current densities**,** action integral for the electromagnetic field**,** inhomogeneous Maxwell equations**,** electromagnetic energy**,** electromagnetic energy-momentum tensor

**Constant electromagnetic fields:** Constant electric fields**,** electrostatic energy of charges**,** electrostatic multipole moments**,** a system of charges in an external electrostatic field**,** constant magnetic fields**,** magnetostatic multipole moments**,** a system of charges in an external magnetostatic field

**Electromagnetic waves:** wave equation and electromagnetic plane waves**,** monochromatic plane waves**,** relativistic Doppler effect**,** spectral analysis**,** group velocity

**Fields of moving charges:** Field of a uniformly moving charge**,** retarded potentials**,** potentials of a moving charge**,** electromagnetic field of a moving charge

**Radiation of electromagnetic waves:** Radiation from a slowly-moving charge**,** dipole radiation**,** bremsstrahlung**,** radiation from a fast-moving charge**,** synchrotron radiation**,** radiation damping

**Organization**

Lectures M W F 11:00 - 11:50 AM

Homework (50%)

Term exam (25% for each of two)

Text: L. D. Landau and E. M. Lifshitz, *The classical theory of fields*

*All information is representative only, and is likely to change from year to year.*