Course syllabus for Vector fields and theory of electromagnetic fields

Course syllabus adopted 2025-02-16 by Head of Programme (or corresponding).

Overview

  • Swedish nameVektorfält och elektromagnetisk fältteori
  • CodeEEN190
  • Credits9 Credits
  • OwnerTKTFY
  • Education cycleFirst-cycle
  • Main field of studyElectrical Engineering, Engineering Physics
  • DepartmentELECTRICAL ENGINEERING
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language Swedish
  • Application code 57126
  • Open for exchange studentsNo

Credit distribution

0122 Examination 9 c
Grading: TH		 1.5 c7.5 c

In programmes

Examiner

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Eligibility

General entry requirements for bachelor's level (first cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Specific entry requirements

The same as for the programme that owns the course.
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Course specific prerequisites

Undergraduate mathematics courses: Multivariable analysis (MVE035 or equivalent), Complex mathematical analysis (MVE025 or equivalent).

Aim

The course aims to provide knowledge of vector analysis and electromagnetic fields, areas that contain basic mathematical methodology, fundamental physics and applications.

Learning outcomes (after completion of the course the student should be able to)

  • Explain the meaning of the basic concepts and operations of mathematical vector analysis, and be able to perform the operations and use this in problem-solving.
  • Explain the meaning of electromagnetic field theory's basic concepts and operations in electrostatics, magnetostatics and electrodynamics, and be able to perform the operations and use this in problem-solving.
  • Explain the connections between the different concepts and use these connections in problem-solving.
  • Combine knowledge of different concepts in practical problem-solving.

Content

Vector fields

  • The concept of vector field in calssical physics, scalar fields and vector fields.
  • Derivation and integration of fields, gradient, divergence, rotation, laplaceoperator, line integral, surface integral, volume integral.
  • Suffix notation. 
  • Sources and curls; superposition, analysis and synthesis of fields.
  • Integral theorems, Gauss' and Stoke's theorems.
  • Singular fields, point source, line sources, rotational fields, delta function.
  • Curvilinear coordinates, scalar factor, derivation operators, integrals.

Electrostatics

  • Charge and charge densities.
  • The electrostatic field, Coulomb's law, Gauss' law, superposition.
  • Electrostatic potential.
  • Electrostatic material models; conductors and insulators, electric dipoles and dipole fields, torque and forces on dipoles in electric fields, polarisation and polarisation charge densities, permittivity, electric displacement, boundary conditions.
  • Electrostatic energy; capacitance calculations, electrostatic energy, energy density, force calculation using the energy method.
  • Boundary value problems; Poisson's and Laplace's equations, uniqueness theorem solution methods.
Magnetostatics

  • Steady electric current density; equation of continuity.
  • Material models; Ohm's law, resistance calculations, boundary conditions, relaxation time, Joule's law.
  • Magnetic flux density, Lorentz force, Ampère's law, superposition, Biot-Savart's law.
  • Magnetic vector potential.
  • Magnetic material models; magnetic dipoles and dipole fields, torque and forces on dipoles in magnetic fields, magnetisation, magnetisation current densities, magnetic field intensity, boundary conditions, ferromagnetic hysteresis.
  • Magnetistatic energy; inductance and mutual inductance, magnetic energy, energy density, force calulations using the energy method.

Electrodynamics

  • Faraday's law of induction.
  • Maxwell's equations, displacement current density, boundary conditions, wave equations, retarded potentials.
  • Complex vector fields and Maxwell's equation on complex form.
  • Plane waves; skin effect, Poynting's theorem, reflection and transmission of plane wave at plane interface, Fresnel equations, Brewster angle, total internal reflection.
  • Antennas; Hertzian dipole, dipole antenna, antenna gain, directivity, radiation resistance, radiation diagram.

Organisation

Lectures, tutorials, problem solving. A non-obligatory "mid-period exam" can give bonus points for the exam. Voluntary web-based hand-in questions every week can give bonus points for the exam.

In SP3 the course is taught together with the course EEF031, Theory of electromagnetic fields.

Literature

Paul C. Matthews: Vector Calculus (Available for free at: https://link.springer.com/book/10.1007/978-1-4471-0597-8)

DK Cheng: Field and Wave Electromagnetics (Pearson New International Edition) 

Supplementary course material is made available on the course webpage.

Examination including compulsory elements

A written exam. Non-obligatory hand-in questions and a voluntary "mid-period exam" give bonus points for the exam.

The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers about disability study support.