Undergraduate Course: Classical Electrodynamics (PHYS11045)
Course Outline
| School | School of Physics and Astronomy |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 11 (Year 4 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 10 |
ECTS Credits | 5 |
| Summary | A course on the Maxwell equations, their Lorentz invariance, covariant formulation, and gauge invariance. Applications included classical radiation from time dependent charges and currents, and in particular accelerating charges. |
| Course description |
* Electrodynamics: Maxwell's equations, charge, energy and momentum conservation, the electromagnetic potentials, electromagnetic radiation and its generation, electric and magnetic dipole radiation.
* Relativity: Lorentz transformations, 4-vectors, relativistic dynamics, the covariant formulation of Maxwell's equations, gauge invariance, magnetism as a relativistic phenomenon, the stress-energy tensor.
* Accelerating charges: covariant Green's functions, the Lienard-Wiechert potential, their associated fields, synchotron radiation, Larmor formula and the Abraham-Lorentz equation.
* Action principles: for point particles, scalar fields, vector fields, Noether's theorem, charge and energy-momentum conservation, the Yukawa potential, radiation vs matter.
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Information for Visiting Students
| Pre-requisites | None |
Course Delivery Information
| Not being delivered |
Learning Outcomes
On completion of the course the student should be able to:
1. understand origin of Maxwell's equations in magnetic and dielectric media
2. write down Maxwell's equations in linear, isotropic, homogeneous media
3. derive continuity conditions on electromagnetic fields at boundaries
4. derive electromagnetic wave solutions and propagation in dielectric and other media
5. understand transport of energy and Poynting vector
6. understand transport of momentum, Maxwell stress tensor and radiation pressure
7. show laws of geometric optics originate with Maxwell's equations at dielectric boundaries
8. calculate reflection and transmission coefficients for waves at dielectric boundaries
9. obtain scalar and vector potential equations in presence of sources
10. understand gauge invariance of Maxwell's equations, decoupling of scalar and vector potential equations in Lorentz gauge and corresponding solutions
11. solve for retarded potentials and electric and magnetic fields for simple problems involving time-dependent charge-current distributions
12. understand the term radiation zone and derive angular distribution of and power emitted by a dipole
13. write down electromagnetic field tensor in covariant notation
14. derive fully covariant forms of Maxwell equations, Lorentz gauge condition and continuity equation
15. obtain Lorentz transformations for electric and magnetic fields and apply to simple cases
16. show the stress-energy-momentum tensor components are energy density, Poynting vector and Maxwell stress tensor
17. derive Lienard-Wiechert potentials for a moving point charge
18. derive corresponding electric and magnetic fields
19. show that acceleration of the charge gives electromagnetic radiation
20. apply to cases of charges: slowly accelerating at low velocities; undergoing acceleration collinear with velocity, in a circular orbit (synchrotron radiation).
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Reading List
| D.J. Griths, Introduction to Electrodynamics, 3rd Edition, Prentice Hall 1999. |
Contacts
| Course organiser | Prof Donal O'Connell
Tel:
Email: |
Course secretary | Miss Paula Wilkie
Tel: (0131) 668 8403
Email: |
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