Introduction to Electromagnetic Fields

a) Lectures

Summary of the fundamentals of electrodynamics, as known from preliminary studies (3 lectures): Source quantities (charge/current density), charge conservation. Vector fields (electric/magnetic field strength, displacement, magnetic flux density) and integral quantities (EMF, MMF, electric/magnetic flux). Lorentz force. Macroscopic effects of electromagnetic fields in medium (polarization, magnetization), material characteristics (permittivity, permeability, specific conductivity). Maxwell's equations in differential and integral form. Continuity of EM fields on material interfaces. Poynting's theorem of energy conservation.

Typical problems of applied electromagnetics, a classification (1 lecture)

Electrostatics (2 lectures): Scalar potential and Laplace-Poisson equation of electrostatics, solution for homogeneous medium. Boundary value problem. Charge substitution, the method of images. Electrodes, capacitance, grounding.

Static current flow (1 lecture): Laplace equation, analogies with electrostatics. The concept of resistance and its generalization for electrode system.

Static magnetic field and induction phenomena (1 lecture): Vector potential and the vectorial Laplace-Poisson equation. Biot-Savart law. Concept of self and mutual inductance. Induction law, transformer/motional EMF.

Transmission lines (1 lecture): Review of what was learned from Signals and Systems 2, interpretation of transmission line parameters in the field theory.

Wave propagation (2 lectures): Phasor representation of vector fields, wave equation for E or H, Helmholtz equation and its plane wave solution. Analogy with transmission lines. Plane waves in dielectric material, polarization, reflection and refraction. Plane waves in good conductors, eddy current phenomena.

Transmission and reception of waves (2 lectures): Inhomogeneous wave equation for the potentials. Field of a Hertzian dipole. Concept of near/far field. Antenna characteristics (demonstrated on the Hertzian dipole).

b) Classroom practices

• Revisiting the necessary mathematical tools (1 exercise)
• Solving simple but relevant analytical calculus problems on the topics covered in the lecture (6 exercises)
• Application of the finite element method to solve boundary value problems; user-level introduction to the Matlab PDE Toolbox (1 exercise)
• Numerical solution of simple two- and three-dimensional field computational problems in the topics covered in the lecture (5 exercises). This will include typical problems in electrostatics, steady currents, magnetic field, eddy currents, wave propagation and scattering.

Exercises using analytical and numerical calculations will be selected according to the current material in the lectures. The exercises will focus on the construction of a practically simplified, i.e. "tractable" mathematical model of the problem and, where relevant, on the mapping of the field computation model to a circuit model and the definition of its parameters. For the numerical calculations, the Matlab PDE Toolbox is generally used; in addition to being able to follow the calculations on a projector, the student can reproduce them on his/her laptop.