The University of Southampton
Courses

# ELEC2210 Applied Electromagnetics

## Module Overview

To introduce the students to fundamental concepts of low frequency electromagnetics with examples from electrical power engineering. To present and develop the concepts of high frequency fields radiated from open and directional antenna systems and wave guides. To give the students an appreciation of the importance of computational electromagnetics in the context of engineering. To introduce the students to fundamental numerical techniques for solving field problems. To equip the students with basic programming, computing and CAD skills. To increase the awareness of the students of the role of mathematics in engineering applications.

### Aims and Objectives

#### Learning Outcomes

##### Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

• Basic concepts of electromagnetic theory
• Principles of finite difference and finite element formulations
• Advantages and limitations of various field modelling techniques
• Techniques of sparse matrices and compact storage schemes
• Vector algebra in the electromagnetic field context
• Properties of static and time-varying electromagnetic fields
• Physical meaning of Maxwell's equations
• Mathematical description of fundamental laws of electromagnetism
• Electric and magnetic properties of matter
• Fundamentals of modelling and simulation techniques applied to electromagnetics
• Dual energy bounds techniques
##### Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

• Appreciate the role of computational electromagnetics in engineering
• Relate field displays to fundamental concepts of electromagnetics
• Identify different types of equations governing electromagnetic processes
• Derive equations describing electromagnetic phenomena
• Formulate fundamental laws of electromagnetism
• Solve differential equations using separation of variables
• Analyse simple electromagnetic systems
• Appreciate the complexity of CAD systems for electromagnetic design
• Distinguish between various stages associated with CAD
• Design models suitable to analyse performance of electromagnetic devices
##### Transferable and Generic Skills

Having successfully completed this module you will be able to:

• Write programs using C language
• Write technical reports
• Work in a small team to conduct an experiment
##### Subject Specific Practical Skills

Having successfully completed this module you will be able to:

• Demonstrate electromagnetic theory applied to simple practical situations
• Explain the meaning and consequences of field theory
• Apply Maxwell's equations to problems involving simple configurations
• Interpret electromagnetic solutions
• Explain the operation of simple electromagnetic devices
• Apply mathematical methods and vector algebra to practical problems
• Be familiar with running commercial finite element software
• Set up, solve and interrogate solutions to problems using FE software

### Syllabus

Approximate methods of field solution (2 lectures) - Geometrical properties of fields; method of ‘tubes and slices’. Flow of steady current (2 lectures) - Potential gradient; current density; divergence; nabla operator; Laplace's equation. Electrostatics (3 lectures) - The electric field vector; scalar electric potential; Gauss's theorem and divergence; conservative fields; Laplace and Poisson equations; electric dipole, line charge, surface charge; solution of Laplace's equation by separation of variables; polarisation; dielectrics, electric boundary conditions. Magnetostatics (4 lectures) - Non-conservative fields, Ampere's law and curl; magnetic vector potential; magnetisation and magnetic boundary conditions; magnetic screening with examples. Electromagneticinduction (2 lectures) - Faraday's law; induced and conservative components of the electric field, emf and potential difference. Maxwell's equations (2 lectures) - Displacement current; Maxwell's and constituent equations; the Lorentz guage; wave equation. Time-varying fields in conductors (3 lectures) - Diffusion and Helmholtz equations; skin depth; eddy currents in slabs, plates and cylindrical conductors; deepbar effect. Computational aspects of approximate methods of field solution (1 lecture) - The method of tubes and slices. Review of field equations (1 lecture) - Classification of fields: Laplace's, Poisson's, Helmholtz, diffusion, wave equations; Vector and scalar formulations. Finite difference method (5 lectures) - Five-point scheme, SOR; example, Diffusion and wave equations, explicit formulation, Crank-Nicholson implicit scheme, a weighted average approximation, alternating-direction implicit method, Convergence and stability, handling of boundary conditions, Alternative formulation of the finite-difference method. Finite element method (5 lectures) - Variational formulation, first-order triangular elements, discretisation and matrix assembly, the art of sparse matrices, alternative approximate formulations (including Galerkin). Electromagnetic radiation (6 lectures) - Current element, radiation resistance, plane waves, linear antenna, antenna arrays, waveguides. Note: the first 30 hours of lectures are common with ELEC2211 and ELEC2219, the last 6 hours are different.

### Learning and Teaching

TypeHours
Follow-up work18
Lecture36
Preparation for scheduled sessions18
Tutorial6
Revision10
Total study time150

F. Ulaby, U. Ravaioli. Fundamentals of Applied Electromagnetics.

Grant, I. S.. Electromagnetism.

Hammond P & Sykulski J K, (1994). Engineering Electromagnetism - Physical Processes andComputation.

Laboratory space and equipment required. Work station in the computing labs, Equipment for the three dedicated laboratory experiments.

Griffiths, David J.. Introduction to electrodynamics.

Christopoulos, Christos. An introduction to applied electromagnetism.

Daniel Fleisch. A Student's Guide to Maxwell's Equations.

John D. Kraus & Daniel A. Fleisch. Electromagnetics with Applications.

Software requirements. Infolytica Magnet; COMSOL multi physics

### Assessment

#### Summative

MethodPercentage contribution
Continuous Assessment 45%
Final Assessment  55%

#### Repeat

MethodPercentage contribution