| CODE | PHY2247 | ||||||||||||||||
| TITLE | Electromagnetism | ||||||||||||||||
| UM LEVEL | 02 - Years 2, 3 in Modular Undergraduate Course | ||||||||||||||||
| MQF LEVEL | 5 | ||||||||||||||||
| ECTS CREDITS | 8 | ||||||||||||||||
| DEPARTMENT | Physics | ||||||||||||||||
| DESCRIPTION | Electromagnetism is a branch of Physics that deals with the electromagnetic force occuring between electrically charged particles. The electromagnetic force is one of the four fundamental forces characterised by electromagnetic fields (magnetic and electric). This study-unit focuses mainly on time-varying electromagnetic (EM) fields and develops the differential form of Maxwell's four equations of electromagnetism that are then used to explain the propagation of EM waves in free space and the interaction of these fields with matter. This leads to establishing the boundary conditions for EM waves at the interface between different materials and subsequent theoretical applications to explain EM field reflection and transmission across these boundaries. Propagation of EM waves in guided structures is also considered (transmission lines and rectangular waveguides). The study-unit concludes with an introduction to radiation theory through the concepts of scalar an vector fields, leading to theoretical analysis of electric and magnetic dipole antennas. Study-unit Aims: This study-unit aims to provide the student with a concrete understanding of the basic principles of electromagnetism and how these evolved from Maxwell's equations in free space and in material media. This will be achieved through providing the opportunity for the students to develop: - a conceptual visualisation of electric, magnetic and electromagnetic fields; - a physical understanding of Maxwell's equations and their implications in various theoretical and practical frameworks; - a basic understanding of electromagnetic field propagation in free space, in linear, isotropic and homogeneous materials and in guided structures; - an introduction to the concepts of radiation theory and how electromagnetic fields are generated by time-varying currents in simple structures (electric and magnetic dipole antennas). Learning Outcomes: 1. Knowledge & Understanding By the end of the study-unit the student will be able to: Electric, magnetic and electromagnetic fields and waves in free space: • derive Gauss’ Laws for static electric fields from charge distributions, starting from Coulomb’s Law; • derive Maxwell’s equation for the divergence of the electric field by applying Gauss’ Law for a charge distribution; • understand the concept of the Lorentz Force; • generalise the differential form of the Biot-Savart Law to obtain an expression for the magnetic flux density from a static current distribution in 3D space; • derive the differential form of Ampere’s Law, starting from the Biot-Savart Law; • modify the equations for the curl of the static electric field E and magnetic flux density B to account for time-variation, leading to the derivation of Maxwell’s equations for the curl of these quantities; • derive the differential form of the continuity equation for electric charge; • understand the concept that a time-varying electric field must be accompanied by a time-varying magnetic field and it’s fundamentally important consequence – electromagnetic waves; • understand the concept of displacement current in free space and its relation to the generation of electromagnetic waves in free space; • derive the wave equation in free space; • recall plane wave solutions for time-varying electric and magnetic fields in free space. • conceptualise polarisation of electromagnetic fields (plane, circular and elliptical). Electric fields in insulators (linear, isotropic media): • understand the concepts of electric dipole moment and dielectric polarisation in insulators, leading to an understanding of external and internal fields in material media; • understand the concept of surface and volume charge densities as the result of uniform and non-uniform external electric fields; • define the electric displacement vector D and electric susceptibility. Magnetic fields in matter (linear, isotropic media): • understand the concepts of the magnetic dipole moment, magnetization vector, magnetic intensity vector H and magnetic susceptibility. Electromagnetic fields in linear, isotropic and homogeneous (LIH) media: • derive Maxwell’s equations in LIH media; • derive the wave equation for LIH media; • provide plane wave solutions for the wave equation in LIH media; • understand these concepts in the context of applications for conducting media - skin depth, electric and magnetic intensity vectors in lossy media, complex permittivity and permeability. Boundary conditions: • derive the boundary conditions for the normal and tangential components of the field vectors E, B, D and H at the interface between two LIH media; • apply the boundary conditions to derive the laws of reflection and transmission between dielectric media; • derive the Fresnel equations, with application to the Brewster angle, and reflection and refraction at the surface of a good conductor. Introduction to guided propagation of electromagnetic waves: • recall the standard waveguide types (coaxial, rectangular, cylindrical, microstrip, ect.); • understand the concept of parallel wire transmission lines, leading to the line equations and the concept of characteristic impedance, impedance matching, reflection and transmission coefficients; • derive the EM fields in rectangular waveguides, TE and TM modes and cut-off frequencies; • represent the current distribution in rectangular waveguides propagating the fundamental TE mode. Radiation theory: • understand the concepts of scalar and vector potentials; • modify Maxwell’s equations in terms of the scalar and vector potentials and provide solutions for these; • understand the concept of the elemental (Hertzian) dipole and be able to derive the near and far field approximations for the corresponding E and H fields; • derive the far field E and H expressions for the half-wavelength antenna and small loop antenna; • understand the concept of radiation resistance of an antenna. 2. Skills By the end of the study-unit the student will be able to: Electric, magnetic and electromagnetic fields and waves in free space: • use the operators of gradient, divergence, curl and the Laplacian effectively. Applying these to understand the Divergence and Stokes’ theorems for application in electromagnetism; • develop an ability to visualise and sketch electric and magnetic fields arising from and around geometrically simple structures; • apply the Divergence theorem to derive Maxwell’s equations for the divergence of the electric field and magnetic flux density; • use Stokes’ theorem to convert the integral form of Ampere’s Law to the differential equivalent involving the curl of the magnetic flux density; • apply Faraday’s Law of Induction to modify to obtain the time-dependent form of the curl of the electric field and its relation to the time derivative of the magnetic flux density, one of Maxwell’s equations; • generalise three dimensional form of the continuity equation for free charges and to derive Maxwell’s equation for the curl of the magnetic flux density; • explain the concept of the displacement current and its implications for transmission of electromagnetic fields in free space; • explain the symmetry between electric and magnetic fields through Maxwell’s equations; • use Maxwell’s equations to derive the wave equations for the electric and magnetic fields in free space; • recall and use three dimensional plane wave solutions for electromagnetic fields in free space and to these represent mathematically in basic polarised forms. Electric fields in insulators: • explain the difference between polar and non-polar dielectric materials; • derive the relation between volume and surface polarisation charge distributions; • derive Maxwell’s divergence equation for the electric field in terms of the electric displacement vector field; • use the relation between the electric field and polarisation vectors to obtain an expression for the electric displacement and hence define electric susceptibility and permittivity. Magnetic fields in matter: • relate magnetic dipole moments on the microscopic scale to the macroscopic magnetic dipole moment per unit volume; • model material magnetisation in terms of surface magnetisation currents; • derive the relation between magnetisation current density and the magnetic dipole moment density, leading to the definition of the magnetic intensity vector; • derive a generalised differential form of Ampere’s Law in terms of the magnetic intensity vector field, leading the definition of magnetic susceptibility. Electromagnetic fields in linear, isotropic and homogeneous (LIH) media: • derive Maxwell’s equations in LIH media, leading to the derivation of the wave equation; • apply plane wave solutions for the wave equation in LIH media in conducting media; • derive the expression for skin depth in conducting media; • represent electric and magnetic intensity vectors in lossy media, leading to general expressions for complex permittivity and permeability. Boundary conditions: • use Maxwell’s equations to derive the boundary conditions for the normal and tangential components of the field vectors E, B, D and H at the interface between two LIH media; • apply the boundary conditions to derive the laws of reflection and transmission between dielectric media; • derive and use the Fresnel equations to obtain the Brewster angle, and apply these to analyse reflection and refraction at the surface of materials, including good conductors. Introduction to guided propagation of electromagnetic waves: • generalise transmission line theory to different types of waveguides; • apply boundary conditions and Maxwell’s equations to rectangular waveguides for TE and TM modes; • derive EM fields in rectangular waveguides, determine cut-off frequencies and characteristic impedance; • acquire experience in carrying out basic laboratory experiments with rectangular waveguides. Radiation theory: • use the concepts of scalar and vector potentials to modify Maxwell’s equations in terms of the scalar and vector potentials and provide solutions for these; • use mathematical techniques to represent phase and amplitude approximations to simplify near and far field expressions for EM fields from elemental, half-wavelength and loop antennas; • describe three dimensional power density from these antennas; • use the concept of radiation resistance of an antenna in the context of antenna matching. Main Text/s and any supplementary readings: Main text: - I. S. Grant & W. R. Phillips, Electromagnetism. John Wiley, 1975 (Second Edition). Additional texts: - R. E. DuBroff, S. V. Marshall & G. G. Skitek, Electromagnetic Concepts and Applications. Prentice Hall, 1996 (Fourth Edition) - W. N. Cottingham & D. A. Greenwood, Electricity and Magnetism. Cambridge University Press, 1991 - P. Lorrain & D. Corson, Electromagnetic Fields and Waves. W.H.Freeman & Co, 1970 - S. Ramo, J. R. Whinery & T. van Duzer, Fields and Waves in Communication Electronics. John Wiley, 1996 - D. H. Staelin, A. W. Morgenthaler & J. A. Kong, Electromagnetic Waves. Prentice Hall, 1994 - J. D. Kraus, Electromagnetics. McGraw-Hill, 1953 (Fourth Edition) - F. W. Ulaby, Fundamentals of Applied Electromagnetics. Prentice-Hall, 2020 - C. A. Balanis, Advanced Engineering Electromagnetics. John Wiley, 1989. |
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| ADDITIONAL NOTES | Pre-Requisite qualifications: Basic knowledge of electric and magnetic fields and associated mathematical background at first year level Pre-Requisite Study-units: First year Electricity and Magnetism and Mathematics for Physicists 1 Co-Requisite Study-units: Mathematics for Physicists 2 |
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| STUDY-UNIT TYPE | Lecture and Tutorial | ||||||||||||||||
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| LECTURER/S | Charles V. Sammut |
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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 description above applies to study-units available during the academic year 2025/6. It may be subject to change in subsequent years. |
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