Module MATH3181: ELECTROMAGNETISM III

Department: Mathematical Sciences

MATH3181: ELECTROMAGNETISM III

Prerequisites

• Analysis in Many Variables II (MATH2031) and Mathematical Physics II (MATH2071); alternatively Analysis in Many Variables (MATH2031) and Foundations of Physics II (PHYS2511).

Corequisites

• None.

Excluded Combination of Modules

• None.

Aims

• To appreciate classical electromagnetism, one of the fundamental physical theories.
• To develop and exercise mathematical methods.

Content

• Electrostatics: Coulomb's law and vector superposition of forces due to different charges.
• Electric fields due to point charges and to volume and surface distributions.
• Electric field E expressed in terms of electrostatic potential.
• Differential equations for the electrostatic field.
• Electric dipoles.
• Dielectric media and electrostatic polarisation.
• Perfect conductors.
• Electrostatic energy.
• Steady magnetics: current density j and conservation of charge, magnetic field B due to a current-carrying loop.
• Differential equations for B.
• Magnetic dipoles.
• Permeable media, magnetisation.
• Time-dependent fields and Maxwell's equations: Faraday's law.
• Maxwell's equations with microscopic sources and in simple media.
• Electromagnetic waves: Plane waves.
• Polarisation.
• Transmission and reflection at plane boundaries.
• Special relativistic formulation of electromagnetism: Maxwell's equations with microscopic sources expressed as tensor equations in Minkowski spacetime.

Learning Outcomes

• By the end of the module students will: be able to solve novel and/or complex problems in Electromagnetism.
• have a systematic and coherent understanding of theoretical mathematics in the field of Electromagnetism.
• have acquired a coherent body of knowledge of these subjects demonstrated through one or more of the following topic areas: General features of electric and magnetic phenomena.
• charge and current densities and charge conservation.
• Electrostatics.
• Time-dependent fields.

• In addition students will have specialised mathematical skills in the following areas which can be used with minimal guidance: modelling

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

• Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
• Assignments for self-study develop problem-solving skills and enable students to test and develop their knowledge and understanding.
• Formatively assessed assignments provide practice in the application of logic and high level of rigour as well as feedback for the students and the lecturer on students' progress.
• The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment:

Four written assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students.

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University