Electromagnetic Field
Code  Completion  Credits  Range  Language 

B1B17EMP  Z,ZK  5  2P+2C  Czech 
 Garant předmětu:
 Vítězslav Pankrác
 Lecturer:
 Vítězslav Pankrác
 Tutor:
 Ladislav Oppl, Vítězslav Pankrác
 Supervisor:
 Department of Electromagnetic Field
 Synopsis:

This course gets its students acquinted with principles and applied electromagnetic field theory basics.
 Requirements:

Basic knowledge of mathematic and physic
 Syllabus of lectures:

1) Basic concepts of electromagnetic theory, nature of electromagnetic phenomena, electromagnetic field produced by electric charges. Macroscopic approach to electromagnetic theory. Solenoidal (divergenceless) and irrotational (potential) vector fields. Classification of materials according to electromagnetic properties.
2) Electrostatic field, Coulomb's Law and electric field intensity E. Gauss's law of electrostatics in integral and differential form, divergence of vector function and divergence theorem.
3) Electric field in conductors and nonconductors (dielectrics). Free charges in conductors, electric flux and electric flux density D. Bound charges in dielectric materials, polarization in dielectrics, electric dipole, electric dipole moment, polarization vector P, electric susceptibility and permittivity.
4) Work done by the electric field, electric potential, potential difference (voltage). Gradient of scalar function. Laplace's and Poisson's equation. Concept of capacitor and capacitance. Electric potential energy due to point charges. Energy stored on capacitor. Electrical energy expressed by E and D.
5) Forces in electric field, principle of virtual work. Dielectricdielectric and conductordielectric boundary conditions. Method of images for calculating electric fields.
6) Stationary current field, electric current and current density, continuity equation, Ohm's law and Joule's law , Boundary condition for current density, electromotive voltage.
7) Magnetostatic Field, magnetic flux density, BiotSavart law, Ampere's circuit law in integral and differential form, curl of vector field
8) Magnetization in materials, equivalent bound volume current, magnetic dipole, Magnetic dipole moment, magnetic field intensity H , magnetization M, magnetic susceptibility, permeability
9) Magnetic flux , static definition of self and mutual inductance, magnetic boundary conditions, method of images for calculating magnetic fields, forces due to magnetic field, calculation of magnetic forces based on principle of virtual work
10) Energy in magnetic field, energy stored in the system of currentcarrying inductors, energetic concept of inductance, Internal and external inductance, energy in magnetic field expressed by B and H
11) Magnetic field in the magnetic circuit, Hopkinson's law, magnetomotive force, reluctance. Faraday's law of induction, Lenz Law. dynamic concept of self and mutual inductance
12) Full set of Maxwell's equations in integral and differential form. Timeharmonic field, fields quantities expressed in phasor form. Poynting's theorem and conservation of energy. Poynting vector.
13) Electromagnetic wave in free space, wave equation, timeharmonic plane wave solution to the wave equation. Propagation constant and wave impedance. Wavelength, phase and group velocity
14) Electromagnetic wave in lossless dielectrics and good conductors. Energy transmitted by electromagnetic waves, polarization of electromagnetic waves. Skin depth, skineffect in conductors and ferromagnetic materials.
 Syllabus of tutorials:

1) Basic mathematical tools for electromagnetics theory:
Scalars and vectors, scalar and vector function, coordinate systems. Vector algebra: Addition and subtraction of vectors, vector multiplication (scalar product, vector product). Line, surface and volume integrals. The flux of a vector field through surface and closed surface, gradient of scalar function, divergence of vector function, GaussOstrogradsky theorem, curl of a vector function, Stoke's theorem.
2) Calculating the electric field of point charges using the superposition principle:
Electric field of a line of charge, electric field on the axis of a ring of charge, electric field on the axis of a disc of charge.
3) Applications of Gauss's Law
Electric field at a point due to infinite line of charge, uniformly charged sphere, uniformly charged infinitely long cylinder, infinite sheet of charge. Electric field of oppositely charged infinite sheets, spheres and long cylinders.
4) Capacitors, capacitance and electric field intensity between two electrodes
Capacitance and electric field of parallel plate capacitor, cylindrical capacitor (coaxial cable) and spherical capacitor
5) Electric potential, method of images
Capacitance of twowire transmission line. Capacitance of a wire or spherical electrode above ground plane. Effect of earth on capacitance of transmission line.
6) Computation of electrostatic forces, using the method of virtual work
7) Stationary current field, examples of resistance calculation
Resistance of cylindrical components. Radial resistance of coaxial cable. Concept and calculation of ground resistance.
8) Magnetostatic fields, superposition of magnetic field generated by current elements according to BiotSavart's law
Magnetic field generated by current in straight wire, magnetic field at a point on axis of circular current loop.
9) Applications of Ampere's law
Magnetic fields around infinite currentcarrying wire, magnetic field inside and around long cylindrical conductor, magnetic field of a coaxial cable.
10) Self and mutual inductance, examples of calculation
The inductance of a coaxial cable, inductance of twowire transmission line, mutual inductance between twowire transmission line and rectangular loop.
11) Magnetic force, Magnetic Circuits
Force between two parallel currentcarrying wires. Calculation of the magnetic circuits, windings on the magnetic circuits, self and mutual inductance of the windings on the ferromagnetic cores.
12) Faraday's law of induction  Application examples
13,14) Timeharmonic electromagnetic plane waves
Properties of electromagnetic waves, calculation of wavelength, phase velocity, wave impedance, propagation constant (attenuation constant, phase constant) in free space or in conductive and dielectric materials.
 Study Objective:

Basic understanding of electromagnetic effects, quantitative estimation of effects, ability to solve simple fields analytically, understanding of numerical electromagnetics field solver principles.
 Study materials:

[1] Pankrác, V.: Základy teorie elektromagnetického pole, výukový materiál k tomuto předmětu (on line), ČVUT Praha
[2] Novotný, K.: Teorie elmag. pole I. Skriptum, ČVUT Praha, 1998
[3] Haňka, L.: Teorie elektromagnetického pole, SNTL, Praha 1975
[4] Mayer, D.: Aplikovaný elektromagnetizmus. Kopp, České Budějovice 2012
[5] Pankrác, V.  Hazdra, P.  Novotný, K.: Teorie elektromagnetického pole ? Příklady, Skriptum ČVUT Praha, 2005
[6] Sadiku, M.N.O.: Elements of Electromagnetics. Saunders College Publishing. London, 1994
[7] Collin, R.E.: Field Theory of Guided Waves. 2nd Edit., IEEE Press, New York 1991
 Note:
 Further information:
 https://moodle.fel.cvut.cz/courses/B1B17EMP
 Timetable for winter semester 2023/2024:

06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon Tue Wed Thu Fri  Timetable for summer semester 2023/2024:
 Timetable is not available yet
 The course is a part of the following study plans:

 Electrical Engineering, Power Engineering and Management  Applied Electrical Engineering 2016 (compulsory course in the program)
 Electrical Engineering, Power Engineering and Management  Electrical Engineering and Management (compulsory course in the program)
 Electrical Engineering, Power Engineering and Management (compulsory course in the program)
 Electrical Engineering, Power Engineering and Management (compulsory course in the program)
 Electrical Engineering, Power Engineering and Management  Applied Electrical Engineering 2018 (compulsory course in the program)
 Electrical Engineering, Power Engineering and Management  Electrical Engineering and Management (compulsory course in the program)