TFY 4108, hausten 2013

Lecture log

This lecture log lists the main topics covered in each lecture and gives references to relevant sections in the textbook (Griffiths; section numbers refer to the 3rd ed.) and Ingve Simonsen's lecture notes (available here). Topics not covered in the textbook (or covered in a very different way) are shown in red.

Date Topics Textbook 2014 notes Other

Wed 11/1 General course information. Vector analysis. Vectors. Coordinate systems. Gradient, divergence, curl, Laplacian. The Einstein summation convention. The Levi-Civita symbol. 1 1 notes

Fri 13/1 Proving vector identities. The divergence theorem and Stokes' theorem. Some results involving the Dirac delta function. Some general issues. Charge and current densities, point charges, the continuity equation. 1, 8.1.1 1

Wed 18/1 The field concept. Maxwell's equations. Macroscopic vs. microscopic equations. Spatial averaging. Microscopic vs. macroscopic description of an interface. Electrostatics. Electric field from a stationary charge distribution. Electric (scalar) potential. Poisson and Laplace equation. Boundary value problems. 2.1-2.3.4 2-2--2-3, 2-6--2-7

Fri 20/1 Electrostatic boundary conditions. Properties of conductors. Boundary value problems for Poisson and Laplace equation. Uniqueness theorem. The method of images. Separation of variables method for Laplace equation: Cartesian coordinates. 2.3.5, 2.5.1, 3.1.5, 3.2, 3.3.1 2-4--2-5, 3-1--3-11

Wed 25/1 Separation of variables method for Laplace equation: Cartesian coordinates (continued). Spherical coordinates with azimuthal symmetry. Legendre polynomials. Spherical coordinates, general case (very brief discussion). Multipole expansion for the electric potential. 3.3, 3.4.1 3-10--3-27, 3-30

Fri 27/1 Multipole expansion (continued). Multipole, dipole, and quadrupole moments. "Pure"/"point" dipole vs. "physical" dipole. Dielectrics. Polarization. Volume and surface polarization (bound) charge. Microscopic theory of polarization: The Lorentz model. 3.4, 4.1, 4.2.1 3-30--3-34, 3-36--3-37, 4-1--4-3

Wed 1/2 Microscopic theories of polarization: (i) The traditional theory (Lorentz model). (ii) The modern theory. Electric field due to bound (polarization) charge. Example: Dielectric sphere with uniform polarization. The D-field (divergence, curl, boundary conditions). Constitutive relations. Simple (linear + isotropic) dielectrics. Example: The field inside a sphere of simple dielectric placed in a uniform external field. 4.2.1, 4.3, 4.4.1 4-3--4-11

Fri 3/2 Examples of field calculations in dielectrics. Potential formulation for dielectrics. Magnetostatics. Magnetic forces. Biot-Savart law. Ampere's law. Magnetic vector potential. 4.4.1, 4.4.2, 5.1-5.3, 5.4.1 4-9--4-11, 5-1--5-11

Wed 8/2 Magnetic vector potential. Gauge transformations, the Coulomb gauge. Surface current density. Magnetostatic boundary conditions. Multipole expansion of the vector potential. Magnetic dipole moment. Magnetic fields in matter. Para-, dia- and ferromagnetism. Electron orbital and spin magnetic moments. 5.4, 6.1.1 5-11--5-20, 6-1--6-2

Fri 10/2 Free current. Bound current and magnetization: Spin, orbital, and total. Volume and surface contributions to bound current. Microscopic theories of magnetization: (i) The traditional theory (Lorentz model) (ii) The modern theory (very brief discussion). The magnetic field due to bound current. 6.1.2, 6.1.4, 6.2.1

Wed 15/2 Physical picture of bound currents. Example: Magnetic field due to sphere with uniform magnetization. The H-field. Boundary conditions. Simple (linear + isotropic) media. Ferromagnetism (very brief discussion, read on your own). Ohm's law, conductivity. Electromotive force (emf). 6.2.2, 6.3, 6.4, 7.1.1, 7.1.2 6-3--6-5, 7-8--7-10

Fri 17/2 Electromotive force (emf). Motional emf. The flux rule. Electromagnetic induction. Faraday's law. Lenz's law. The induced electric field. Mutual inductance, self-inductance. Displacement current, Ampere-Maxwell law. Maxwell's equations. Scalar and vector potentials. 7.1.2, 7.1.3, 7.2.1-7.2.3, 7.3.1-7.3.3, 10.1.1 7-10--7-16, 7-5--7-7

Wed 22/2 The polarization current. Maxwell's equation in matter. Boundary conditions. Charge conservation. Energy conservation, the Poynting vector. 7.3.5, 7.3.6, 8.1.1, 8.1.2 7-1--7-5, 8-1--8-6

Fri 24/2 Scalars. Vectors. Tensor (outer) product of two vectors. Tensors of rank 2. The dot product between a rank-2-tensor and a vector. Symmetric tensors. "Tensor generalization" of the divergence theorem. Tensors of rank > 2. Field momentum and momentum conservation in electrodynamics (motivation). 8.2.1 8-7--8-15

Wed 1/3 Force density. The Maxwell stress tensor. Total force on charges inside a volume. Pressure and shear forces. Example: Maxwell stress tensor for two charged cylinders. 8.2.2 8-16--8-19 Example: Maxwell stress tensor for two charged cylinders

Fri 3/3 Momentum density in EM fields. Conservation of momentum. The cross product between a rank-2-tensor and a vector. Electromagnetic angular momentum density and angular momentum current density, local conservation of angular momentum (very brief discussion). Classical wave equation. Sinusoidal waves. Complex notation. Wave polarization. Electromagnetic (EM) waves in vacuum. Wave equation for E- and B-fields. Monochromatic plane EM waves and their properties. 8.2.3, 8.2.4, 9.1.1, 9.1.2, 9.1.4, 9.2.1-9.2.3 8-20--8-27, 9-1--9-9

Wed 8/3 Energy and momentum in EM waves in vacuum. Time-averaged quantities. Intensity. Radiation pressure. Averages of products expressed in the complex notation. EM waves in simple nonconducting media. Reflection and transmission at a flat interface between two such media. TM (p) and TE (s) linear polarization. 9.2.3, 9.3.3 9-10--9-17

Fri 10/3 Laws of reflection and refraction (Snell's law). Fresnel equations for p-polarization. Brewster's angle. Intensities, reflection and transmission coefficients for p-polarization. Total internal reflection, s-polarization (very brief discussions). EM waves in conductors. 9.3.2, 9.3.3, 9.4.1 9-27--9-39

Wed 15/3 EM waves in conductors: Attenuation, skin depth, relative magnitude and phase for E and B fields, complex dielectric function, reflection at a conducting surface (very brief discussion). Frequency dependence, dispersion. Ohm's law for time-dependent problems. The Drude model for conductors. 9.4.1, 9.4.2, 9.4.3 9-40--9-44, 9-46

Fri 17/3 The Drude model for conductors: opacity at low frequencies, transparency at high frequencies, plasma oscillations. The Lorentz model for dielectrics: frequency dispersion (normal and anomalous), energy absorption. Wave packets: shape distortion, group velocity. Response functions: causality, the connection between real and imaginary parts. Guided waves. Optical fibers (total internal reflection). 9.4.3, 9.5.1 9-47, 9-55

Wed 22/3 Hollow metallic wave guide. TE/TM/TEM waves. TE waves in rectangular wave guide. Scalar and vector potentials. Differential equations for the potentials. Gauge transformations. 9.5.1, 9.5.2, 10.1.1, 10.1.2 9-56--9-61, 10-1--10-6

Fri 24/3 The Coulomb and Lorenz gauges. Inhomogeneous wave equations in the Lorenz gauge. The Green function method. Green functions for the Laplacian and d'Alembertian operators. Retarded and advanced Green functions, causality. The retarded potentials for arbitrary sources, the retarded time. 10.1.3, 10.2.1 10-7--10-17 ("note-02" about Green functions is also relevant)

Wed 29/3 Jefimenko's equations for E and B. The (Lienard-Wiechert) potentials for a moving point charge. The associated E- and B-fields (started the derivation). 10.2.2, 10.3.1, 10.3.2 10-22--10-32

Fri 31/3 The (Lienard-Wiechert) E- and B-fields for a moving point charge (finished the derivation). Properties of the "acceleration" and "velocity" contributions. Radiation, radiated power. Radiation fields from an electric dipole. 10.3.2, 11.1.1, 11.1.2 10-33--10-35, 11-1--11-10, 11-20

Wed 5/4 No lecture (excursion week).

Fri 7/4 No lecture (excursion week).

Wed 19/4 Electric dipole radiation. Magnetic dipole radiation (very brief discussion). Radiation from an arbitrary localized source: leading (electric dipole) contribution (very brief discussion). Radiation from a point charge. The Larmor formula. 11.1, 11.2.1 11-11--11-13, 11-22--11-23, 11-28--11-33

Fri 21/4 Lienard's relativistic generalization of the Larmor formula. Radiation for velocity parallel/perpendicular to acceleration. Radiation reaction (very brief discussion). Special relativity (very brief discussion): Lorentz transformations, 4-vectors, transformation properties of the E- and B-fields. A previous exam problem. 11.2.1, 11.2.2, 12.1.3-12.1.4, 12.3.2-12.3.5 11-34--11-36

Date	Topics	Textbook	2014 notes	Other
Wed 11/1	General course information. Vector analysis. Vectors. Coordinate systems. Gradient, divergence, curl, Laplacian. The Einstein summation convention. The Levi-Civita symbol.	1	1	notes
Fri 13/1	Proving vector identities. The divergence theorem and Stokes' theorem. Some results involving the Dirac delta function. Some general issues. Charge and current densities, point charges, the continuity equation.	1, 8.1.1	1
Wed 18/1	The field concept. Maxwell's equations. Macroscopic vs. microscopic equations. Spatial averaging. Microscopic vs. macroscopic description of an interface. Electrostatics. Electric field from a stationary charge distribution. Electric (scalar) potential. Poisson and Laplace equation. Boundary value problems.	2.1-2.3.4	2-2--2-3, 2-6--2-7
Fri 20/1	Electrostatic boundary conditions. Properties of conductors. Boundary value problems for Poisson and Laplace equation. Uniqueness theorem. The method of images. Separation of variables method for Laplace equation: Cartesian coordinates.	2.3.5, 2.5.1, 3.1.5, 3.2, 3.3.1	2-4--2-5, 3-1--3-11
Wed 25/1	Separation of variables method for Laplace equation: Cartesian coordinates (continued). Spherical coordinates with azimuthal symmetry. Legendre polynomials. Spherical coordinates, general case (very brief discussion). Multipole expansion for the electric potential.	3.3, 3.4.1	3-10--3-27, 3-30
Fri 27/1	Multipole expansion (continued). Multipole, dipole, and quadrupole moments. "Pure"/"point" dipole vs. "physical" dipole. Dielectrics. Polarization. Volume and surface polarization (bound) charge. Microscopic theory of polarization: The Lorentz model.	3.4, 4.1, 4.2.1	3-30--3-34, 3-36--3-37, 4-1--4-3
Wed 1/2	Microscopic theories of polarization: (i) The traditional theory (Lorentz model). (ii) The modern theory. Electric field due to bound (polarization) charge. Example: Dielectric sphere with uniform polarization. The D-field (divergence, curl, boundary conditions). Constitutive relations. Simple (linear + isotropic) dielectrics. Example: The field inside a sphere of simple dielectric placed in a uniform external field.	4.2.1, 4.3, 4.4.1	4-3--4-11
Fri 3/2	Examples of field calculations in dielectrics. Potential formulation for dielectrics. Magnetostatics. Magnetic forces. Biot-Savart law. Ampere's law. Magnetic vector potential.	4.4.1, 4.4.2, 5.1-5.3, 5.4.1	4-9--4-11, 5-1--5-11
Wed 8/2	Magnetic vector potential. Gauge transformations, the Coulomb gauge. Surface current density. Magnetostatic boundary conditions. Multipole expansion of the vector potential. Magnetic dipole moment. Magnetic fields in matter. Para-, dia- and ferromagnetism. Electron orbital and spin magnetic moments.	5.4, 6.1.1	5-11--5-20, 6-1--6-2
Fri 10/2	Free current. Bound current and magnetization: Spin, orbital, and total. Volume and surface contributions to bound current. Microscopic theories of magnetization: (i) The traditional theory (Lorentz model) (ii) The modern theory (very brief discussion). The magnetic field due to bound current.	6.1.2, 6.1.4, 6.2.1
Wed 15/2	Physical picture of bound currents. Example: Magnetic field due to sphere with uniform magnetization. The H-field. Boundary conditions. Simple (linear + isotropic) media. Ferromagnetism (very brief discussion, read on your own). Ohm's law, conductivity. Electromotive force (emf).	6.2.2, 6.3, 6.4, 7.1.1, 7.1.2	6-3--6-5, 7-8--7-10
Fri 17/2	Electromotive force (emf). Motional emf. The flux rule. Electromagnetic induction. Faraday's law. Lenz's law. The induced electric field. Mutual inductance, self-inductance. Displacement current, Ampere-Maxwell law. Maxwell's equations. Scalar and vector potentials.	7.1.2, 7.1.3, 7.2.1-7.2.3, 7.3.1-7.3.3, 10.1.1	7-10--7-16, 7-5--7-7
Wed 22/2	The polarization current. Maxwell's equation in matter. Boundary conditions. Charge conservation. Energy conservation, the Poynting vector.	7.3.5, 7.3.6, 8.1.1, 8.1.2	7-1--7-5, 8-1--8-6
Fri 24/2	Scalars. Vectors. Tensor (outer) product of two vectors. Tensors of rank 2. The dot product between a rank-2-tensor and a vector. Symmetric tensors. "Tensor generalization" of the divergence theorem. Tensors of rank > 2. Field momentum and momentum conservation in electrodynamics (motivation).	8.2.1	8-7--8-15
Wed 1/3	Force density. The Maxwell stress tensor. Total force on charges inside a volume. Pressure and shear forces. Example: Maxwell stress tensor for two charged cylinders.	8.2.2	8-16--8-19	Example: Maxwell stress tensor for two charged cylinders
Fri 3/3	Momentum density in EM fields. Conservation of momentum. The cross product between a rank-2-tensor and a vector. Electromagnetic angular momentum density and angular momentum current density, local conservation of angular momentum (very brief discussion). Classical wave equation. Sinusoidal waves. Complex notation. Wave polarization. Electromagnetic (EM) waves in vacuum. Wave equation for E- and B-fields. Monochromatic plane EM waves and their properties.	8.2.3, 8.2.4, 9.1.1, 9.1.2, 9.1.4, 9.2.1-9.2.3	8-20--8-27, 9-1--9-9
Wed 8/3	Energy and momentum in EM waves in vacuum. Time-averaged quantities. Intensity. Radiation pressure. Averages of products expressed in the complex notation. EM waves in simple nonconducting media. Reflection and transmission at a flat interface between two such media. TM (p) and TE (s) linear polarization.	9.2.3, 9.3.3	9-10--9-17
Fri 10/3	Laws of reflection and refraction (Snell's law). Fresnel equations for p-polarization. Brewster's angle. Intensities, reflection and transmission coefficients for p-polarization. Total internal reflection, s-polarization (very brief discussions). EM waves in conductors.	9.3.2, 9.3.3, 9.4.1	9-27--9-39
Wed 15/3	EM waves in conductors: Attenuation, skin depth, relative magnitude and phase for E and B fields, complex dielectric function, reflection at a conducting surface (very brief discussion). Frequency dependence, dispersion. Ohm's law for time-dependent problems. The Drude model for conductors.	9.4.1, 9.4.2, 9.4.3	9-40--9-44, 9-46
Fri 17/3	The Drude model for conductors: opacity at low frequencies, transparency at high frequencies, plasma oscillations. The Lorentz model for dielectrics: frequency dispersion (normal and anomalous), energy absorption. Wave packets: shape distortion, group velocity. Response functions: causality, the connection between real and imaginary parts. Guided waves. Optical fibers (total internal reflection).	9.4.3, 9.5.1	9-47, 9-55
Wed 22/3	Hollow metallic wave guide. TE/TM/TEM waves. TE waves in rectangular wave guide. Scalar and vector potentials. Differential equations for the potentials. Gauge transformations.	9.5.1, 9.5.2, 10.1.1, 10.1.2	9-56--9-61, 10-1--10-6
Fri 24/3	The Coulomb and Lorenz gauges. Inhomogeneous wave equations in the Lorenz gauge. The Green function method. Green functions for the Laplacian and d'Alembertian operators. Retarded and advanced Green functions, causality. The retarded potentials for arbitrary sources, the retarded time.	10.1.3, 10.2.1	10-7--10-17 ("note-02" about Green functions is also relevant)
Wed 29/3	Jefimenko's equations for E and B. The (Lienard-Wiechert) potentials for a moving point charge. The associated E- and B-fields (started the derivation).	10.2.2, 10.3.1, 10.3.2	10-22--10-32
Fri 31/3	The (Lienard-Wiechert) E- and B-fields for a moving point charge (finished the derivation). Properties of the "acceleration" and "velocity" contributions. Radiation, radiated power. Radiation fields from an electric dipole.	10.3.2, 11.1.1, 11.1.2	10-33--10-35, 11-1--11-10, 11-20
Wed 5/4	No lecture (excursion week).
Fri 7/4	No lecture (excursion week).
Wed 19/4	Electric dipole radiation. Magnetic dipole radiation (very brief discussion). Radiation from an arbitrary localized source: leading (electric dipole) contribution (very brief discussion). Radiation from a point charge. The Larmor formula.	11.1, 11.2.1	11-11--11-13, 11-22--11-23, 11-28--11-33
Fri 21/4	Lienard's relativistic generalization of the Larmor formula. Radiation for velocity parallel/perpendicular to acceleration. Radiation reaction (very brief discussion). Special relativity (very brief discussion): Lorentz transformations, 4-vectors, transformation properties of the E- and B-fields. A previous exam problem.	11.2.1, 11.2.2, 12.1.3-12.1.4, 12.3.2-12.3.5	11-34--11-36