# Study-Unit Description

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CODE PHY2145

TITLE Electromagnetism

LEVEL 02 - Years 2, 3 in Modular Undergraduate Course

ECTS CREDITS 4

DEPARTMENT Physics

DESCRIPTION Electrostatics: Coulomb’s Law, electric field of a charge distribution, Gauss’ Law, the divergence of E.

Steady currents - magnetostatics: Lorentz force, Biot-Savart Law, the divergence of B, Ampère’s Law.

Time-varying fields: Faraday’s Law of Induction, the curl of E, vacuum displacement current, and the curl of B.

Electromagnetic waves in free space: Maxwell’s equations in free space, wave equations for E and B, plane wave solutions for the wave equation, polarization.

Electric fields in insulators: electric dipole moment, dielectric polarization, dielectrics in non-uniform electric fields, polarization charge density and surface charge density, the electric displacement vector D, electric susceptibility.

Magnetic fields in matter: magnetic dipole moment, the magnetization vector M, the magnetic intensity vector H, magnetic susceptibility.

Electromagnetic fields in linear, isotropic and homogeneous (LIH) media: Maxwell’s equations in LIH media, the wave equation for LIH media, conducting media, skin depth, E and H vectors in lossy media, complex permittivity and permeability.

Electromagnetic field energy: energy density in electromagnetic fields, energy flow, Poynting’s Theorem, the Poynting Vector in free space and in LIH media.

Boundary conditions: boundary conditions at the interface between two LIH media for the field vectors E, B, D and H.

Basic applications of the Boundary Conditions: reflection and refraction of plane waves at the interface between dielectric media, the Fresnel equations, the Brewster angle, reflection and refraction at the surface of a good conductor.

Introduction to guided propagation of electromagnetic waves: types of waveguides, parallel wire transmission lines, the line equations, characteristic impedance, rectangular waveguides, transverse electric and transverse magnetic propagation modes in rectangular waveguides, cutoff frequency.

Study-unit Aims:

The central aim of this study-unit is to provide students of physics with a broad and basic background in electromagnetic theory. This will be achieved specifically through the following aims:
- review of electrostatics and magnetostatics with the introduction of vector calculus in three dimensions as applied to the derivation of Coulomb's, Gauss', Lorentz force, Biot-Savart and Ampère’s Laws as well as Maxwell's equations for the divergence of the field vectors E and B;
- consideration of time-varying fields, leading to Maxwell's equations for the curl of E and B, and the consequent implication of the existence of electromagnetic fields in free space, derivation of the wave equation in free space and plane wave solutions for this;
- consideration of E and B fields in matter will lead to the concepts of the field vectors D and H, electric and magnetic susceptibility, permittivity and permeability of materials and the consequent adaptation of Maxwell's equations for LIH media, from which it would be possible to derive the wave equation in LIH media and consider attenuation;
- derivation of the boundary conditions for plane EM waves at plane boundaries will lead to basic applications, such as the laws of reflection and refraction, derivation of the Fresnel equations, etc. These will form the basic concepts for guided propagation in simple configuration (transmission lines and rectangular waveguides).

Learning Outcomes:

1. Knowledge & Understanding
By the end of the study-unit the student will be able to:

- recall and derive Maxwell's equations in free space;
- use Maxwell's equations to derive the wave equation in free space and to substitute plane wave solutions to derive an expression for the phase velocity of EM waves in free space;
- understand and graphically represent the relative directions of the E, B and k vectors in a propagating plane wave and have a basic understanding of polarisation;
- consider E and B fields in matter, define the field vectors D and H and apply these to derive basic expressions for electric and magnetic susceptibilities, leading to the concepts of relative permittivity and permeability;
- derive the wave equation for LIH media, substitute plane wave solutions and obtain expressions for the complex wave number, leading to the concept of attenuation;
- distinguish between two general loss mechanisms in materials - dielectric and magnetic polarisation, and conduction loss;
- consider energy flow in EM waves, derive and interpret Poynting's theorem, define, interpret and use the Poynting vector;
- derive, recall and use the boundary conditions for the field vectors E, B, D and H;
- apply the boundary conditions and Maxwell's equations to explain the laws of reflection, refraction and to apply these to analyse simple guided propagation.

2. Skills
By the end of the study-unit the student will be able to:

- demonstrate competence in mathematical skills as applied to the derivation of Maxwell's equations and to solve problems involving the application of these equations in different situations;
- improve problem-solving skills, especially applied to electromagnetism;
- represent EM fields by complex exponential expressions and manipulate these in various contexts in order to address the aims of the study unit;
- derive, interpret with physical understanding and apply a number of equations leading to the aims of the study unit.

Main Text/s and any supplementary readings:

Main text:

- S. GRANT & W. R. PHILLIPS: Electromagnetism, 2nd Edition, Wiley

Supplementary:

- W. N. COTTINGHAM & D. A. GREENWOOD: Electricity and Magnetism, Cambridge University Press
- R. E. DuBROFF, S. V. MARSHALL & G. G. SKITEK: Electromagnetic Concepts and Applications, Fourth Edition, Prentice Hall
- P. LORRAIN & D. CORSON: Electromagnetic Fields and Waves, W. H. Freeman & Co.
- S. RAMO, J. R. WHINERY & T. van DUZER: Fields and Waves in Communication Electronics, Wiley
- D. H. STAELIN, A. W. MORGENTHALER & J. A. KONG: Electromagnetic Waves, Prentice Hall
- J. D. KRAUS: Electromagnetics, Fourth Edition, McGraw-Hill
- F. W. ULABY: Fundamentals of Applied Electromagnetics, Prentice-Hall
- C. A. BALANIS: Advanced Engineering Electromagnetics, John Wiley

STUDY-UNIT TYPE Lecture, Independent Study & Tutorial

METHOD OF ASSESSMENT
 Assessment Component/s Assessment Due Resit Availability Weighting Examination (2 Hours) SEM2 Yes 100%

LECTURER/S Julian Bonello

The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints.
Units not attracting a sufficient number of registrations may be withdrawn without notice.
It should be noted that all the information in the study-unit description above applies to the academic year 2019/0, if study-unit is available during this academic year, and may be subject to change in subsequent years.

https://www.um.edu.mt/course/studyunit