Synopsis for B7.2b: Special Relativity and Electromagnetism

Level: H-level Method of Assessment: Written examination.
Weight: half-unit (cannot be taken unless B7.1a is taken) (OSS paper code 2A87)
Prerequisites: B7.1a Quantum Mechanics

Recommended Prerequisites:

Part A Quantum Theory,

Overview

Maxwell's electromagnetic theory revealed light to be an electromagnetic phenomenon whose speed of propagation proved to be observer-independent. This discovery led to the overthrow of classical Newtonian mechanics, in which space and time were absolute, and its replacement by Special Relativity and space-time. The aim of this course is to study Einstein's special theory of relativity, to understand space-time, and to incorporate into it Maxwell's electrodynamics. These theories together with quantum theory are essential for an understanding of modern physics.

Synopsis

Constancy of the speed of light. Lorentz transformations and the invariance of the wave operator; time dilation, length contraction and the relativistic Doppler effect; the resolution of the simple 'paradoxes' of relativity. Four-vectors, four-velocity and four-momentum; equivalence of mass and energy; particle collisions and four-momentum conservation; four-acceleration and four-force, the example of the constant-acceleration world-line. Contravariant and covariant vectors and tensors; index notation.

Solving Poisson's equation and the wave equation with sources. Derivation of Maxwell's equations with sources from a variational principle.

Electromagnetism in four-dimensional form; the electromagnetic field tensor; the transformation las for the electric and magnetic fields; the Lorentz force law; the electromagnetic four potential and the energy-momentum tensor.

The preferred text is:

1. N. M. J. Woodhouse, Special Relativity (Springer, 2002).
2. N. M. J. Woodhouse, General Relativity (Springer, 2006).

An alternative is:

1. W. Rindler, Introduction to Special Relativity (2nd edition, Oxford University Press 1991).

Additional Reading

For the experimental background to special relativity, and in many libraries:

1. A. P. French, Special Relativity (MIT Introductory Physics Series, Nelson Thornes, 1971).

For advanced texts on electromagnetism, see:

1. W. J. Duffin, Advanced Electricity and Magnetism (McGraw–Hill, 1968).
2. J. D. Jackson, Classical Electromagnetism (Wiley, 1962).