Applied Mathematics
MP366: Electromagnetism (5 ECTS)
(This course will be run every other year.) This course introduces the theory of electromagnetism. Topics covered include electrostatics, the electrostatics of materials, magnetostatics, the magnetostatics of materials, and a brief introduction to Maxwell's laws.
Taught in Semester(s) I. Examined in Semester(s) I.
Workload: 36 hours (24 Lecture hours, 12 Tutorial hours).
Module Learning Outcomes.
On successful completion of this module the learner should be able to:
- calculate electric fields for distributions of point charges, make rough sketches of electric field lines for some simple charge distributions;
- calculate electric fields in geometries with high symmetry using Gauss's law, calculate the capacitance of some standard capacitors;
- approximate electric fields at large distances from a charge source using a multipole expansion;
- calculate the electric field and polarization in linear dielectrics with simple geometries by solving boundary value problems;
- calculate magnetic fields for some simple systems by direct integration;
- calculate magnetic fields for systems with high symmetry using Ampere's law;
- derive the wave equation from Maxwell's laws in vacuum in the absence of sources;
- construct plane wave solutions to Maxwell's equations in vacuum and calculate the energy associated with such solutions.
Indicative Content
This course introduces the theory of electromagnetism.
The material covered includes:
(i). Electrostatics: Coulomb's law, the superposition principle, field lines, electric flux, Gauss's law, calculation of electric fields using Gauss's law, the electric potential and Poisson's equation, electrostatic energy, conductors, boundary condition for conductors, capacitors, calculating the capacitance for some simple geometries;
(ii). Electrostatics of materials: Legendre polynomials and multipole expansions, the electric dipole, dielectric atoms and molecules, polarization, macroscopic electrostatic equations, linear dielectrics and their boundary conditions, the solution of some boundary value problems;
(iii). Magnetostatics: current density, conservation of charge, steady currents, Orsted's experiment, the Lorentz force law, the Biot-Savart law, Ampere's law and examples of its use, the differential equations of magnetostatics, some calculations for magnetic fields, magnetic field due to a localised current distribution, magnetic dipole moment, torque on a current loop, brief discussion of magnetic materials and the macroscopic magnetostatic equations;
(iv). Electromagnetism: Ohm's law, electromotive force, Faraday’s experiments and Faraday’s law, Maxwell's laws, Poynting's theorem and electromagnetic energy, the wave equation and the electromagnetic character of light, plane wave solutions of Maxwell's laws.
Module Resources
- Introduction to Electrodynamics, 3rd edition, D. J. Griffith, Prentice Hall
- Electricity and Magnetism, Berkeley Physics Course, Volume 2, 2nd edition., E.M. Purcell, McGraw Hill
- Lectures on Physics, Volume II, R.P. Feynman, R.B. Leighton & M. Sands, 50th anniversary edition, Basic Books
- Classical Electrodynamics, 3rd edition, J.D. Jackson, John Wiley & Sons
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