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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, Biot-Savart, 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.
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This course is a pre-master 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, Biot-Savart, 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 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 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 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:
- 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
- Biot-Savart’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 self-induction, 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
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| Largely Calculus A and B, in particular multi-dimensional integrals and vector-calculus. |
| Bachelor Electrical Engineering |
| | Required materialsCourse material| D.J. Griffiths, "Introduction to Electrodynamics", 4th edition, Addison-Wesley, ISBN 978-0321856562 |
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Recommended materials-Instructional modesTestsExam
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