Electromagnetic Field Theory
Learning Outcomes
On completion of the course the student shall be able to:
- formulate potential problems within electrostatics, magnetostatics and stationary
current distributions in linear, isotropic media, and also solve such problems in simple
geometries using separation of variables and the method of images
- define and derive expressions for the energy both for the electrostatic and
magnetostatic fields, and derive Poyntings theorem from Maxwells equations and
interpret the terms in the theorem physically
- describe and make calculations of plane electromagnetic waves in homogeneous
media, including reflexion of such waves in plane boundaries between homogeneous
media
- account for the relation between circuit equations (Kirchoff's laws) and Maxwells
equations
Content
Repetition of vector analysis. Repetition of the electrostatic and magnetostatic fields,
including the polarisation field in dielectrics and the magnetisation field in magnitisible
media. Potential theory (boundary value problems, uniqueness theorem, method of
images, separation of variables) with applications in electrostatics, magnetostatics
and stationary current distributions. Induction law and dispacement current.
Transformation of the electromagnetic field. Maxwells equations. Poyntings theorem.
Wave equation, plane waves and a brief description of waves along different types of
wave guides. Field penetration in conducting media. Skin depth. Generation of
electromagnetic radiation (inhomogeneous wave equation, retarded potentials).
Electric dipole radiation field. Derivation of circuit equations (Kirchoff's laws) from
Maxwells equations.
Guest lecture.
Instruction
Lectures and lessons.
Assessment
Written examination at the end of the course.
Classical Electrodynamics
Learning Outcomes
On completion of the course the student shall be able to:
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interpret the deeper meaning of the Maxwellian field equations and account for
their symmetry and transformation properties, domain of validity, and
limitations
formulate and solve electromagnetic problems with the help of electrodynamic
potentials and superpotentials, and make a detailed account for gauge
transformations and their use
master the techniquue of deriving and evaluating formulae for the
electromagnetic fields from very general charge and current distributions
calculate the electromagnetic radiation from radiating systems (aerials,
localised charge and current distributions) at rest
calculate the electromagnetic radiation from localised charges which move
arbitrarily in time and space, taking into account retardation effects. Account
for the underlying approximations and assumptions
formulate and solve electrodynamic problems in relativistically covariant form
in four-dimensional spacetime
formulate self-consistent models för the interaction between matter and
electromagnetic fields in relativistically covariant Lagrange and Hamilton
formalism
be familiar with some elementary phenomena and concepts in quantum
electrodynamics
Content
Maxwell´s equations. Energy and momentum formula in Maxwell´s theory. Maxwell´s
stress tensor, radiation pressure. Telegraph equation. EM waves in vacuum and in
media. Phase and group velocity, dispersion. The inhomogenious wave equation.
Gauge transformations, gauge invariance. Retarded potentials. Fields from random
distributions of currents and charges. Super potentials. Electric and magnetic
multipole radiation. Relativistic kinematics. Covariant formulation of electrodynamics.
Liénard-Wiechert´s potentials. Fields from a charged particle at random motion.
Brehmsstrahlung, cyclotron and synchrotron radiation. Coherens and incoherens.
Vavilov-Cerenkov radiation. Virtual photons. Radiation attenuation. Scattering from
an individual charged particle. Absorption of radiation in an oscillator. Rayleigh
scattering. Dispersion relations. Relativistic Lagrange and Hamilton formalism for
charged particles in a field. Lagrange and Hamilton covariant equations for classical
EM fields and interaction with charged particles. Periodic solutions in a box. Plane
wave representation.
Instruction
Lectures, lessons and demonstration of computer simulations, project.
Assessment
Written examination at the end of the course. Project. Passed assignments may give
bonus in the exam.