
The student:
 Can apply abstract vector calculus in the context of electric and magnetic fields.
 Can understand the physical essence of the four Maxwell equations in a broader context. Can relate these to the associated empirical laws of Coulomb, BiotSavart, Lorentz, Ampere and Faraday, including the superposition principle.
 Gains an instinctive understanding of the structure of electric and magnetic fields and gains an understanding of the meaning and use of the Coulomb and vector potential.
 Is able to make efficient use of integral and differential laws and operations, and is able to choose suiting coordinate systems for the calculation of fields and potentials in typical and basic, mostly symmetric situations where charge and current distributions are given.
 Can understand the basic effects that rule the behavior of dielectric and magnetic matter when placed in electric and magnetic fields.
 Oversees basic conservation laws for energy and charge and oversees the origin and basic properties of electromagnetic waves.



This course is a premaster course for Nanotechnology and Electrical Engineering.
This course teaches the physics of the electric and magnetic phenomena and the phenomena that interconnect these. The course describes the phenomena initially separately, by recalling the empirical laws of Coulomb, BiotSavart, Ampere, and of induction. Next, these laws are expressed in terms of vector calculus. Line, surface and volume integrals are applied to better reveal the physics behind these phenomena and to reveal the properties and spatial structure of the associated scalar and vector fields. The course begins with Coulomb’s law, introduces Gauss’ law (differential and integral), and the electrostatic potential (differential and integral) and field energy. Subsequently, the properties of metals and dielectrics in electric fields and the polarization and the dielectric displacement fields are introduced. The magnetostatic phenomena are introduced in analogy, starting with BiotSavart’s law and the Lorentzforce, followed by Ampere’s law (differential and integral) and the magnetic vectorpotential (differential and integral). After a brief introduction of the magnetic properties of matter (magnetization and magnetic induction fields), the connection between electric and magnetic phenomena is drawn in a first step via Ohm’s law, and then electrodynamics is introduced via the two laws of mutual induction (both in integral and differential form). The four obtained Maxwellequations are analyzed with their constitutional equations, to derive the existence of electromagnetic waves and some basic properties. The course is partly consisting of lectures to provide an overview, guidance and general understanding. In the other part, homework questions are discussed in smaller groups, and solutions are presented and explained during seminars. The following subjects are treated:
 Vector fields, gradient, divergence, curl, integrals of vector fields over lines/curves/surfaces
 Coulomb’s law, line, surface and volume charge distributions
 Structure of electrostatic fields, definition of field flux and Gauss law
 The electrostatic potential, Laplace and Poisson equation
 Polarization of matter, linear dielectrics, forces and torque on dipoles
 Polarization and the dielectric displacement field, capacitance, energy in electric fields
 BiotSavart’s and Lorentz’ laws: line, surface and volume currents, continuity equation
 Structure of magnetic fields, Ampere’s law, the vector potential
 Magnetization of matter, force and torque on magnetic dipoles
 Magnetization and the magnetic induction field,
 Ohm’s law, electromotive force, electric circuits, Faraday’s law of induction, Lenz’ rule, magnetic selfinduction, energy in magnetic fields, and Maxwell’s correction to Ampere’s law
 Maxwell’s equations in vacuum, Poynting’s theorem
 Plane, monochromatic electromagnetic waves, polarization, energy flow, momentum flow




 Assumed previous knowledgeLargely Calculus A and B, in particular multidimensional integrals and vectorcalculus. 
Bachelor Electrical Engineering 
  Required materialsCourse materialD.J. Griffiths, "Introduction to Electrodynamics", 4th edition, AddisonWesley, ISBN 9780321856562 

 Recommended materialsInstructional modesTestsExam


 