Department of Physics, Unit Catalogue 2007/08 |
PH40068 Mastering electromagnetism |
| Credits: 6 |
| Level: Masters |
| Semester: 2 |
| Assessment: EX80CW20 |
| Requisites: |
| Before taking this unit you must take PH20014 and take PH20020 and in taking this unit you cannot take PH30023 |
|
Aims: The aims of this unit are to develop a full formal vectorial description of electric, magnetic and electromagnetic fields in infinite materials, to analyse the polarisation and magnetisation vector fields of arbitrary shaped samples, and to derive the general boundary conditions between materials. A further aim is to use these tools to derive some individual solutions and to make use of them in a few important applications: radiation, transmission, reception and guidance of electromagnetic energy.
Learning Outcomes: After taking this unit the student should be able to: * manipulate full vectorial versions of Maxwell's equations in static and time-varying cases * analyse in detail the propagation of vectorial plane waves in vacuum and in various materials (e.g. lossy dielectrics, metals and plasmas) * derive the details of the polarisation and magnetisation vectors in materials * match electric and magnetic fields at boundaries between materials (including the effects of surface charge densities and currents) and explain the origins of Brewster's angle, total internal reflection and tunnelling * calculate the energy density in static and time-varying fields * derive and make use of the electromagnetic Poynting vector * use static and time-varying scalar and vector potentials to calculate electric, magnetic and electromagnetic fields * outline the basic features of electric and magnetic dipoles * analyse the modes of rectangular metallic waveguides (cut-off, total number of modes, impedance, power flow) * describe some simple antennas and analyse their basic characteristics using magnetic vector potentials. Skills: Numeracy T/F A, Problem Solving T/F A. Content: Mathematical review: vector calculus; div, grad, curl; divergence and Stokes' theorem. Maxwell's equations: Differential form of "static" Maxwell equations from Gauss, Biot-Savart and Ampere Laws. Time variations; Faraday's Law, the continuity equation and vacuum displacement current. Solutions in infinite vacuum: The wave equation. Plane wave solutions and properties; polarisation, impedance. Electromagnetic energy. Poynting's theorem. Radiation pressure. Solutions in infinite materials: Concepts of linearity, isotropy and homogeneity. Characterisation of materials in terms of macroscopic parameters. Dipoles, susceptibility and polarisation / magnetisation vectors fields. Capacitors. The modified wave equation; solution in conductors, dielectrics, lossy media and plasma. Boundaries between media: The general electromagnetic boundary conditions. Plane waves at a planar boundary; general angle of incidence (Fresnel equations). Brewster and critical angles. Coefficients of transmission and reflection at normal incidence. Radiation: Electromagnetic potentials; retarded potentials; near and far fields; radiation from a Hertzian dipole; simple antennas and antenna arrays. Guided waves: The rectangular metal pipe waveguide. |