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Full Year

Electromagnetism and Relativity (PHYS10093)

Subject

Physics and Astronomy

College

SCE

Credits

20

Normal Year Taken

3

Delivery Session Year

2023/2024

Pre-requisites

Knowledge of vector calculus is essential; some knowledge of electromagnetism and special relativity is desirable but not essential

Course Summary

This is a two-semester course, which begins with a lengthy preparatory section on vectors, matrices, tensors, fields and their symmetries using suffix notation and the Einstein summation convention. The remainder of the first semester covers electrostatics and magnetostatics, using vector calculus techniques. In the second semester we complete the set of four Maxwell equations by studying time-dependent electromagnetic phenomena such as induction and electromagnetic waves. The last part of the course introduces the four-vector formulation of special relativity and the covariant form of Maxwell's equations.The course follows on from the second-year courses Introductory Fields and Waves and Introductory Dynamics. It provides a good starting point for SH/IM field theory courses, in particular Classical Electrodynamics, General Relativity, and Quantum Field Theory.

Course Description

Semester 1: Kinematics, Electrostatics and Magnetostatics:- Vectors, bases, Einstein summation convention, the delta & epsilon symbols, matrices, determinants. [1]- Rotations of bases, composition of two rotations, reflections, projection operators, passive and active transformations, the rotational symmetry group. [2]- Cartesian tensors: definition/transformation properties and rank, quotient theorem, pseudo- tensors, the delta and epsilon symbols as tensors. [2]- Examples of tensors: moment of inertia tensor, rotation of solid bodies, stress and strain tensors, and elastic deformations of solid bodies, ideal fluid flow. [3]- Electric charge and charge density: Coulombs law: linear superposition, Electrostatic potential: equipotentials: derivation of Gauss' Law in integral and differential form, Electrostatic Energy: Energy in the electric field, Electric dipoles: Force, Torque and Energy for a Dipole: the Multipole expansion. [3]- Perfect conductors: surface charge: pill box boundary conditions at the surface of a conductor: uniqueness theorem: boundary value problems, Linear dielectrics: D and E, boundaries between dielectrics, boundary value problems. [3]- Currents in bulk, surfaces, and wires, current conservation: Ohms Law, conductivity tensor: EMF [2]- Forces between current loops: Biot-Savart Law for the magnetic field, Ampere's Law in differential and integral form, pill-box boundary conditions with surface currents. [2]- The vector potential: gauge ambiguity: magnetic dipoles: magnetic moment and angular momentum: force and torque on magnetic dipoles. [2]- Magnetization: B and H, boundaries between magnetic materials, boundary- value problems. [2]Semester 2: Dynamics, Electromagnetism and Relativity:- Dynamics of point particles in gravitational, electric and magnetic fields, inertial systems, Invariance under Galilean translations and rotations. [1]- Motional EMF: Lenz's Law: Faraday's Law in integral and differential form, mutual Inductance: Self Inductance: Energy stored in inductance: Energy in the magnetic field, simple AC circuits (LCR): use of complex notation for oscillating solutions, impedance. [3]- The displacement current and charge conservation: Maxwell's Equations, Energy conservation from Maxwell's eqns: Poynting vector, Momentum conservation for EM fields: stress tensor: angular momentum. [3]- Plane Wave solutions of free Maxwell equations: prediction of speed of light, Polarization, linear and circular, in complex notation: energy and momentum for EM waves. [2]- Plane waves in conductors: skin depth: reflection of plane waves from conductors, Waveguides and cavities: lasers, Reflection and refraction at dielectric boundaries: derivation of the Fresnel equations, Interference and diffraction, single and double slits. [3]- Physical basis of Special Relativity: the Michelson-Morley experiment, Einstein's postulates, Lorentz transformations, time dilation and Fitzgerald contraction, addition of velocities, rapidity, Doppler effect and aberration, Minkowski diagrams. [3]- Non-orthogonal co-ordinates, covariant and contravariant tensors, covariant formulation of classical mechanics, position, velocity, momentum and force 4 vectors, particle collisions. [2]- Relativistic formulation of electromagnetism from the Lorentz force, Maxwell tensor, covariant formulation of Maxwell's equations, Lorentz transformation of the electric and magnetic fields, invariants, stress energy tensor, the electromagnetic potential, Lorenz gauge. [3]- Generation of radiation by oscillating charges: wave equations for potentials: spherical waves: causality: the Hertzian dipole. [2]

Assessment Information

Written Exam 80%, Coursework 20%, Practical Exam 0%

Additional Assessment Information

80% exam 20% coursework

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