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Outline:

This module aims to: discuss the electric and magnetic properties of materials; establish Maxwell's equations of electromagnetism, and use them to derive electromagnetic wave equations; understand the propagation of electromagnetic waves in vacuo, in dielectrics and in conductors; explain energy flow (Poynting's theorem), momentum and radiation pressure, the optical phenomena of reflection, refraction and polarization, discussing applications; use the retarded vector potential to understand the radiation from an oscillating dipole; understand how electric and magnetic fields behave under relativistic transformations.

Aims:

This module aims to:

• Discuss the magnetic and electric properties of materials
• Build on the contents of the second year module PHAS0021 Electricity and Magnetism, to establish Maxwell's equations of electromagnetism, and use them to derive electromagnetic wave equations
• Understand the propagation of electromagnetic waves in vacuo, in dielectrics and in conductors
• Explain energy flow (Poynting's theorem), momentum and radiation pressure, the optical phenomena of reflection, refraction and polarization, discussing various applications including radiation from moving charge
• Use the retarded vector potential to understand the radiation from an oscillating dipole
• Understand how electric and magnetic fields behave under relativistic transformations

Intended Learning Outcomes:

After completing the module the student should be able to:

• understand the relationship between the E, D and P fields, between the B, H and M fields
• be able to derive the continuity conditions for B and H at boundaries between media; distinguish between diamagnetic, paramagnetic and ferromagnetic behaviour
• use the vector potential A in the Coulomb gauge to calculate the field due to a magnetic dipole
• calculate approximate values for the B and H fields in simple electromagnets
• understand the need for displacement currents
• explain the physical meaning of Maxwell's equations, in both integral and differential form, and use them to; (i) derive the wave equation in vacuum and the transverse nature of electromagnetic waves; (ii) account for the propagation of energy and for radiation pressure; (iii) determine the reflection, refraction and polarization amplitudes at boundaries between dielectric media, and derive Snell's law and Brewster's angle; (iv) establish the relationship between relative permittivity and refractive index; (v) explain total internal reflection; (vi) derive conditions for the propagation of electromagnetic waves in, and reflection from, metals; (vii) derive the dispersion relation for the propagation of waves in a plasma, and discuss its relevance to radio communication
• understand how an oscillating dipole emits radiation and use the vector potential in the Lorentz gauge to calculate fields and energy fluxes in the far-field; understand how accelerating charges emit radiation and the relevance of retarded potentials
• be able to transform electric and magnetic fields between inertial frames

Teaching and Learning Methodology:

This course is delivered via weekly lectures, usually supplemented by a series of problem solving classes.

In addition to timetabled lecture and supplementary hours, it is expected that students engage in self-study in order to master the material. This can take the form, for example, of practicing example questions and further reading in textbooks and online, and consulting the pre-recorded videos which cover the lecture content.

Indicative Topics:

1. Introduction and revision of mathematical methods and electricity and magnetism for static problems.
2. Macroscopic fields.
3. Atomic mechanisms.
4. Ferromagnetism.
5. Maxwell's Equations and Electromagnetic Waves.
6. Reflection and Refraction.
7. Waves in Conducting Media.
8. Energy Flow and the Poynting vector.
9. Emission of Radiation.
10. Relativistic Field Transformations