Upon completion of this course the student will be able to:
- Understand the physical essence of the four Maxwell equations in a broader context, and
- To relate the Maxwell equations to the empirical laws of Coulomb, Biot-Savart, Lorentz and Ampere, including the principle of superposition,
- Have an instinctive understanding of the structure of electric and magnetic fields and understands the meaning and use of the Coulomb and vector potential,
- Make efficient use of integral and differential laws and operators, and is able to choose a suitable coordinate system for the calculation of fields and potentials in typical, mostly symmetrical situations in which charge and current distribution are given,
- Understand the basic effects that determine the behaviour of dielectric and magnetic materials when they are placed in electric and magnetic fields and are able to quantify the associated displacement and induction fields and the associated bound charge and currents,
- Oversee the conservation laws for energy and charge and contain the origin and simple properties of electromagnetic waves.
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, Biot-Svart, 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. The properties of metals and dielectrics in electric fields, the polarization and the dielectric displacement fields are introduced after multi-pole expansion of the Coulomb potential. The magneto-static phenomena are introduced in analogy, starting with Biot-Savart’s law and the Lorentz-force, followed by Ampere’s law (differential and integral) and the magnetic vector-potential (differential and integral). After 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 Maxwell-equations 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:
- Coulomb’s law, line, surface and volume charge distributions,
- Structure of electrostatic fields, definition of field flux and Gauss law,
- The electrostatic potential and its multi-pole expansion, Laplace and Poisson equation,
- Polarization of matter, linear dielectrics, forces and torque on dipoles,
- Bound surface and volume charge, the dielectric displacement field and boundary conditions, capacitance, energy in electric fields,
- Biot-Savart’s and Lorentz’ laws: line, surface and volume currents, continuity equation,
- Structure of magnetic fields, Ampere’s law, the vector potential and multi-pole expansion,
- Magnetization of matter, force and torque on magnetic dipoles,
- Bound surface and volume currents, the magnetic induction field and boundary conditions,
- Ohm’s law, electromotive force, electric circuits, Faraday’s law of induction, Lenz’ rule, magnetic self-induction, energy in magnetic fields, and Maxwell’s correction to Ampere’s law,
- Maxwell’s equations in vacuum and in dielectric matter, Poynting’s theorem,
- Plane, monochromatic electromagnetic waves, polarization, energy flow, momentum flow.
|Bachelor Applied Mathematics||Required materials|
Recommended materials-Instructional modes
|D.J. Griffiths, Introduction to electrodynamics, 4th edition, Addison-Wesley. ISBN 978-0321856562|