PH3007 Electromagnetism

Further information on which modules are specific to your programme.

Module description

The properties of electromagnetic fields will be explored using a variety of mathematical tools (in particular, vector and differential calculus). Topics will include: charge and current distributions, electro- and magnetostatics, materials, electrodynamics, conservation principles and electromagnetic waves. This module builds on knowledge and skills acquired in prior coursework by developing techniques for solving more advanced problems in electromagnetism.

Additional information from school

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PH3007 - Electromagnetism

Overview

The properties of electromagnetic fields are explored using a variety of mathematical tools (in particular, vector and differential calculus). Topics include: time-independent charge and current distributions, electric and magnetic properties of matter, electrodynamics, conservation laws, electromagnetic waves and radiation.

Aims & Objectives

This module builds on knowledge and skills acquired in prior courses, to develop more sophisticated techniques for solving problems in undergraduate electromagnetism.

The various topics will be presented as part of a coherent theory of classical fields (i.e., as consequences of Maxwell's equations and the Lorentz force law).

The organisation and level of difficulty of the module have been chosen so as to deepen students' understanding of electromagnetic theory, prepare them for practical work in the laboratory, and provide a bridge to more advanced study.

Alongside the development of general problem-solving skills and intellectual maturity, emphasis will be placed on conceptual understanding, and deriving physical meaning from mathematical expressions and visual representations.

Learning Outcomes

By the end of this module, students are expected to be able to:

• use Maxwell’s equations in integral form to derive expressions for the fields due to charge/current distributions having planar, cylindrical or spherical symmetry.

• calculate electro-magnetostatic fields by direct integration of Coulomb’s law and the Biot-Savart law; and determine time-independent scalar and vector potentials through a variety of techniques (e.g., method of images, multipole expansion).

• translate between E- & B-fields and the auxiliary fields D & H, in terms of the polarisation and magnetisation of a material; and be able to derive (from Maxwell's equations) and apply the boundary conditions on E, B, D & H at the interface of two different linear media.

• explain how Poynting’s theorem is an expression of local energy conservation, and use its mathematical expression to solve problems involving the transport of energy by electromagnetic fields.

• derive wave equations (and their solutions) for electromagnetic fields in free space and in matter, starting from Maxwell's Equations.

• determine the boundary conditions for EM waves at the interface of two different linear media, starting from Maxwell's Equations, and apply them to solve for and interpret the reflected and transmitted waves.

Synopsis

Electrostatics: Charge and current distributions; Coulomb’s law; Gauss’ law; potential theory; linear dielectrics.

Magnetostatics: Biot-Savart law, Ampere’s law; vector potential; magnetic fields in matter.

Electrodynamics: Maxwell’s equations; electromagnetic induction; conservation laws for charge and energy; Poynting vector; wave equation; time-dependent potentials and gauge invariance; dipole radiation; reflection and transmission.

Additional information on continuous assessment etc.

Please note that the definitive comments on continuous assessment will be communicated within the module.  This section is intended to give an indication of the likely breakdown and timing of the continuous assessment.

This module is part of the core JH programme, and as such there is a summary of deadlines etc on the School’s Students and Staff web pages. There is a class test, likely in week seven, contributing 15% to the module mark, Students have compulsory tutorials every two weeks, with hand-in tutorial work counting for 5% of the module total. 

Accreditation Matters

This module contains some material that is or may be part of the IOP “Core of Physics”.  This includes

Electrostatics and magnetostatics

Gauss, Faraday, Ampère, Lenz and Lorentz laws to the level of their vector expression

Maxwell’s equations and plane EM wave solution; Poynting vector

Polarisation of waves and behaviour at plane interfaces

Recommended Books

Please view University online record: http://resourcelists.st-andrews.ac.uk/modules/ph3007.html

General Information

Please also read the general information in the School's honours handbook that is available via st-andrews.ac.uk/physics/staff_students/timetables.php.