### Electromagnetic Fields

#### Course Description

The circuit concept, which was presented in subjects "Fundamentals of Electrical Engineering" and "Electric circuits", is expanded to a multi-dimensional field concept based on Maxwell equations. The themes are: Lorentz force, electric field strength, magnetic flux density. Sources: charge and current. Charge at rest: Coulomb s law, Gauss s law, energy and potential in electric field. Dielectrics, conductors, capacitance. Charge in uniform motion: Ohm s law, resistance. Biot-Savart s law, Ampere s circuital law, magnetic materials, energy in magnetic field, inductances, magnetic circuits. Time-dependent fields, Faraday s law, sinusoidal fields. Displacement currents, Maxwell equations, electromagnetic waves.

#### General Competencies

Understanding multi-dimensional approach to analysis of electromagnetic phenomena. Knowledge of fundamental laws of electromagnetism formulated by Maxwell equations, and their application to practical problems.

#### Learning Outcomes

1. Explain fundamental laws of electromagnetism (Coulomb's, Biot-Savart, Faraday's and Gauss's law).
2. Apply the fundamental laws of electromagnetism to solution of electromagnetic field problems.
3. Classify problems of electromagnetic fields into static electric, static magnetic, static current and dynamic fields.
4. Recognize advantages of application of numerical approach to solution of electromagnetic problems.
5. Apply calculation of electromagnetic fields, inductances and capacitances to solution of practical problems.
6. Describe fundamental operating principles of transformers, motors and generators.
7. Explain the relationship between electromagnetic fields and circuit elements.
8. Analyze how energy is stored and transported in an electromagnetic field.

#### Forms of Teaching

Lectures

Involment in lectures

Exams

Computer aided, written, amd oral exams

Laboratory Work

Laboratory work

Consultations

Lecturers consultations

By decision of the Faculty Council, in the academic year 2019/2020. the midterm exams are cancelled and the points assigned to that component are transferred to the final exam, unless the teachers have reassigned the points and the grading components differently. See the news for each course for information on knowledge rating.

Continuous Assessment Exam
Laboratory Exercises 0 % 10 % 0 % 10 %
Quizzes 0 % 6 % 0 % 6 %
Mid Term Exam: Written 0 % 30 % 0 %
Final Exam: Written 0 % 30 %
Final Exam: Oral 24 %
Exam: Written 24 % 60 %
Exam: Oral 24 %

#### Week by Week Schedule

1. Fundamental postulates: conservation of charge. Lorentz force: electric field strength, magnetic induction. Charge in motion in electric and magnetic field. Macroscopic and microscopic approach. Field sources: charge and current. Volume, surface, line and point sources. Continuity equation. Static electric field in vacuum. Coulomb's law.
2. Electric field strength. Electric field of point charge and of continuous charge distributions. Electric flux. Gauss's law. Potential in electric field, voltage. Integral equations of potential of point charge and of continuous charge distributions. Visual presentation of electric field: field lines and equipotentials.
3. Relationship between field strength and potential. Curl of electric field. Materials in electric field. Field and charge in a conductor.
4. Polarization of dielectric, vector of electric flux density and permittivity. Boundary conditions. Laplace’s and Poisson’s differential equation of potential. Method of images in static electric field. Energy in electric field: system of point charges, volume charge density, energy expressed by field vectors.
5. Condensers and capacity. Energy in condenser. Forces in electric field. Laboratory 1: Coulomb's law, permittivity. Energy in electric fields (experiments).
6. Charge in uniform motion - first Kirchhoff's law. Equations of static current field - analogies and imaging. Conductor-insulator boundary conditions. Ohm’s law, resistance. Joule's law. Electromotive force - second Kirchhoff's law. Static magnetic field in vacuum. Biot-Savart's law. Magnetic force on the current carrying conductor. Magnetic flux, Gauss's law. Laboratory 2: Application of numerical finite element software software in calculation of static electric fields
7. Mid-term exam
8. Mid-term exam
9. Ampere’s circuital law. Magnetic vector potential: differential and integral equation of potential. Visual presemtation of magnetic filed. Magnetic materials, magnetization.
10. Magnetic field strength and permeability, types of magnetic materials, permanent magnets. Boundary conditions. Energy in magnetic field: current loop in magnetic field, system of current loops, energy expressed by field vectors, energy in linear and non-linear materials. Inductance and mutual inductance.
11. Forces in magnetic field. Magnetic circuits.Laboratory 3: Magnetic field on the axis of a multilayer air-core solenoid. Energy of a linear solenoid. Hysteresis (experiments).
12. Quasistatic fields. Faraday’s law of electromagnetic induction: voltage induced in a conductor which is moving in static magnetic field, voltage induced in static loop which is in quasistatic field. Lenz's rule. Applications: generator, transformer. Voltages induced due to self-induction and mutual induction. Eddy currents. Laboratory 4: Application of numerical finite element software in calaculation of magnetic circuits.
13. Extension of Ampere's circuital law, displacement current. Maxwell’s equations in differential and integral form. Energy and power flow. Poynting’s theorem.
14. Sinusoidal time varying fileds. Energy and power flow, Poynting's theorem. Electromagnetic waves in free space. Plane wave. Constants of wave propagation: impedance, wave length, phase velocity, phase constant. Laboratory 5: Transformer. Helmholtz coils. Levitating ring. Velocity of electromagnetic waves in dielectric (experiments).
15. Electromagnetic waves in real dielectrics and conductors. Attenuation constant and depth of penetration. Energy flow. Classification of materials to dielectrics and conductors. Skin effect. Polarization. Laboratory 6: Application of finite element software in calculation of a levitating ring.

#### Study Programmes

Electrical Engineering and Information Technology (study)
(4. semester)

#### Literature

Z. Haznadar, Ž. Štih (1997.), Elektromagnetizam I, Školska knjiga
Z. Haznadar, Ž. Štih (1997.), Elektromagnetizam II, Školska knjiga
S. Berberović (1998.), Teorijska elektrotehnika - odabrani primjeri, Graphis Z. Haznadar, Ž. Štih (2000.), Electromagnetic Fields, Waves and Numerical Methods, IOS Press S.V. Marshall, G.G. Skitek (1990.), Electromagnetic Concepts and Applications, Prentice-Hall
(.), Engineering Electromagnetics W.H. Hayt McGraw Hill 1988,

#### General

ID 86459
Summer semester
6 ECTS
L3 English Level
L1 e-Learning
75 Lectures
0 Exercises
15 Laboratory exercises
0 Project laboratory