Electromagnetic Field

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Code Completion Credits Range Language
B2B17EMPA Z,ZK 5 2P+2C Czech
Garant předmětu:
Vítězslav Pankrác
Vítězslav Pankrác
Pavel Hazdra, Ladislav Oppl, Vítězslav Pankrác, Samuel Trávníček
Department of Electromagnetic Field

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


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. Dielectric-dielectric and conductor-dielectric 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, Biot-Savart 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 current-carrying 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. Time-harmonic field, fields quantities expressed in phasor form. Poynting's theorem and conservation of energy. Poynting vector.

13) Electromagnetic wave in free space, wave equation, time-harmonic 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, skin-effect 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, Gauss-Ostrogradsky 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 two-wire 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 Biot-Savart'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 current-carrying 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 two-wire transmission line, mutual inductance between two-wire transmission line and rectangular loop.

11) Magnetic force, Magnetic Circuits

Force between two parallel current-carrying 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) Time-harmonic 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

Further information:
Time-table for winter semester 2023/2024:
Pankrác V.
(lecture parallel1)
Pankrác V.
(lecture parallel1
parallel nr.102)

Pankrác V.
(lecture parallel1
parallel nr.105)

Hazdra P.
(lecture parallel1
parallel nr.104)

Oppl L.
(lecture parallel1
parallel nr.101)

Trávníček S.
(lecture parallel1
parallel nr.103)

Time-table for summer semester 2023/2024:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2024-02-23
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