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).

Date Topics Textbook 2014 notes Other

Tue 18/8 Nabla operator. Levi-Civita tensor. Vector calculus. Dirac delta function. 1 1

Fri 21/8 Electrostatics. Uniqueness theorem for Laplace and Poisson equations. 2, 3.1 2, 3-1

Tue 25/8 Method of images. Laplace equation: Cartesian coordinates. 3.2, 3.3 3-2--3-13

Fri 28/8 Laplace equation: Cartesian, spherical, and cylindrical coordinates. 3.3 3-13--3-29

Tue 1/9 Multipole expansions (lecture cancelled, read on your own). 3.4 3-30--3-37

Fri 4/9 Laplace eq: Cylindrical coordinates. Multipole expansions (summary). Electric fields in matter. Dielectrics. Polarization. The D-field. 3.4, 4.1-4.3 3-30--3-37, 4-1--4-5 Laplace eq in cylindrical coordinates

Tue 8/9 The D-field. Constitutive relations. Linear media. Volume and surface bound charge. Boundary conditions. Energy density. Fundamental eqs. of magnetostatics. 4.2-4.4 4-4--4-13

Fri 11/9 Continuity equation. Magnetic forces. Biot-Savart law. Ampere's law. Magnetic vector potential. Gauge transformations. 5.1-5.4 5-1--5-14

Tue 15/9 Surface current density. Magnetostatic boundary conditions. Multipole expansion of the vector potential. Magnetic fields in matter. Para-, dia- and ferromagnetism. 5.1.3, 5.4.2, 5.4.3, 6.1 5-15--5-20, 6-1--6-2

Fri 18/9 Magnetization. The field of a magnetized object. Bound currents and their physical interpretation. The H-field. Boundary conditions. Linear media. Ferromagnetism (very brief discussion, read on your own). Ohm's law, conductivity. 6.1.4, 6.2-6.4, 7.1.1 6-1--6-6, 7-8--7-9

Tue 22/9 Aside: Solution of problem 2 in tutorial 3. Electromotive force (emf). Motional emf. The flux rule. Electromagnetic induction. Faraday's law. Lenz's law. The induced electric field. 7.1.2, 7.1.3, 7.2.1, 7.2.2 7-10--7-13

Fri 25/9 The induced electric field. Mutual inductance, self-inductance. Displacement current, Ampere-Maxwell law. Maxwell's equations. Scalar and vector potentials. Polarization current. Maxwell's equations in matter. Linear isotropic media. Boundary conditions. The continuity equation. 7.2.2-7.2.3, 7.3.1-7.3.3, 7.3.5-7.3.6, 8.1.1 7-1--7-7, 7-14--7-16, 8-1

Tue 29/9 Conservation laws in classical electrodynamics. Charge conservation (the continuity equation). Energy conservation (Poynting's theorem). The Poynting vector. Tensors. 8.1.1, 8.1.2 8-1--8-8

Friday 2/10 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. Field momentum and momentum conservation in electrodynamics (motivation). 8.2.1, 8.2.2 8-8--8-14

Tuesday 6/10 Tensors with rank > 2 (forgotten last time). Force density. The Maxwell stress tensor. Total force on charges inside a volume. Pressure and shear forces. Momentum density in EM fields. Conservation of momentum. Example: Maxwell stress tensor for two charged cylinders. 8.2.2, 8.2.3 8-15--8-20, 8-22--8-23 Example: Maxwell stress tensor for two charged cylinders

Friday 9/10 Example (continued). 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. 8.2.2, 8.2.4, 9.1.1, 9.1.2, 9.1.4, 9.2.1, 9.2.2 8-19, 8-26--8-27, 9-1--9-8

Tuesday 13/10 (Only 1 hour lecture, the 2nd hour was used for the numerical project.) Energy and momentum in EM waves in vacuum. Time-averaged quantities. Intensity. Radiation pressure. Averages of products expressed in the complex notation. 9.2.2, 9.2.3 9-8--9-13

Friday 16/10 EM waves in linear nonconducting media. Reflection and transmission at a flat interface between two such media. TM (p) and TE (s) linear polarization. Laws of reflection and refraction (Snell's law). Fresnel equations for p-polarization. Brewster's angle. 9.3.1, 9.3.3 9-14, 9-16--9-17, 9-27, 9-34

Tuesday 20/10 Intensities, reflection and transmission coefficients for p-polarization. Total internal reflection, s-polarization (very brief discussions). EM waves in conductors: Attenuation, skin depth, phase difference between E and B fields, complex dielectric function. Dispersion: wave shape distortion, phase velocity, group velocity. 9.3.3, 9.4.1, 9.4.3 9-42--9-44, 9-46--9-47

Friday 23/10 "Anomalous" dispersion. Guided waves. Optical fibers (total internal reflection). Hollow metallic wave guide. TE/TM/TEM waves. TE waves in rectangular wave guide. Scalar and vector potentials. 9.4.3, 9.5.1, 9.5.2, 10.1.1 9-46--9-47, 9-55--9-61, 10-1--10-3

Tuesday 27/10 Inhomogeneous wave equations for the potentials. Gauge transformations. The Coulomb and Lorenz gauges. Properties of the potentials in the Lorenz gauge, the retarded time. The Green function method. Green functions for the Laplacian and d'Alembertian operators. 10.1.1-10.1.3, 10.2.1 10-3--10-10, 10-13--10-15 ("note-02" about Green functions is also relevant)

Friday 30/10 Retarded and advanced Green functions, causality. The retarded potentials for arbitrary sources. The associated E- and B-fields (Jefimenko's equations). The (Lienard-Wiechert) potentials for a moving point charge. The associated E- and B-fields (started the derivation). 10.2.1, 10.2.2, 10.3.1, 10.3.2 10-16--10-17, 10-22--10-33

Tuesday 3/11 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. Electric dipole radiation. 10.3.2, 11.1.1, 11.1.2 10-33--10-34, 11-1--11-3, 11-9, 11-20

Friday 6/11 Electric dipole radiation. Magnetic dipole radiation (very brief discussion). Radiation from an arbitrary localized source. 11.1.2-11.1.4 11-9--11-15, 11-17

Tuesday 10/11 Lecture cancelled. The time between 11:15 and 12:00 was used for an extra tutorial hour.

Friday 13/11 Multipole expansion for the vector potential of an arbitrary localized source. The n=0 term: electric dipole radiation. The n=1 term: magnetic dipole and electric quadrupole radiation (very brief discussion). Radiation fields from a point charge. 11.1.4, 11.2.1 11-15--11-23, 11-26--11-27, 11-28--11-31

Tuesday 17/11 Radiation from a point charge. The Larmor formula and Lienard's relativistic generalization. Radiation reaction (very brief discussion). Special relativity (very brief discussion): Lorentz transformations. 4-vectors. Transformation properties of the E- and B-fields. End of new material, started repetition. 11.2.1, 11.2.2, 12.1.3, 12.1.4, 12.3.2-12.3.5 11-29--11-35

Friday 20/11 Repetition. A previous exam problem (brief discussion).

Date	Topics	Textbook	2014 notes	Other
Tue 18/8	Nabla operator. Levi-Civita tensor. Vector calculus. Dirac delta function.	1	1
Fri 21/8	Electrostatics. Uniqueness theorem for Laplace and Poisson equations.	2, 3.1	2, 3-1
Tue 25/8	Method of images. Laplace equation: Cartesian coordinates.	3.2, 3.3	3-2--3-13
Fri 28/8	Laplace equation: Cartesian, spherical, and cylindrical coordinates.	3.3	3-13--3-29
Tue 1/9	Multipole expansions (lecture cancelled, read on your own).	3.4	3-30--3-37
Fri 4/9	Laplace eq: Cylindrical coordinates. Multipole expansions (summary). Electric fields in matter. Dielectrics. Polarization. The D-field.	3.4, 4.1-4.3	3-30--3-37, 4-1--4-5	Laplace eq in cylindrical coordinates
Tue 8/9	The D-field. Constitutive relations. Linear media. Volume and surface bound charge. Boundary conditions. Energy density. Fundamental eqs. of magnetostatics.	4.2-4.4	4-4--4-13
Fri 11/9	Continuity equation. Magnetic forces. Biot-Savart law. Ampere's law. Magnetic vector potential. Gauge transformations.	5.1-5.4	5-1--5-14
Tue 15/9	Surface current density. Magnetostatic boundary conditions. Multipole expansion of the vector potential. Magnetic fields in matter. Para-, dia- and ferromagnetism.	5.1.3, 5.4.2, 5.4.3, 6.1	5-15--5-20, 6-1--6-2
Fri 18/9	Magnetization. The field of a magnetized object. Bound currents and their physical interpretation. The H-field. Boundary conditions. Linear media. Ferromagnetism (very brief discussion, read on your own). Ohm's law, conductivity.	6.1.4, 6.2-6.4, 7.1.1	6-1--6-6, 7-8--7-9
Tue 22/9	Aside: Solution of problem 2 in tutorial 3. Electromotive force (emf). Motional emf. The flux rule. Electromagnetic induction. Faraday's law. Lenz's law. The induced electric field.	7.1.2, 7.1.3, 7.2.1, 7.2.2	7-10--7-13
Fri 25/9	The induced electric field. Mutual inductance, self-inductance. Displacement current, Ampere-Maxwell law. Maxwell's equations. Scalar and vector potentials. Polarization current. Maxwell's equations in matter. Linear isotropic media. Boundary conditions. The continuity equation.	7.2.2-7.2.3, 7.3.1-7.3.3, 7.3.5-7.3.6, 8.1.1	7-1--7-7, 7-14--7-16, 8-1
Tue 29/9	Conservation laws in classical electrodynamics. Charge conservation (the continuity equation). Energy conservation (Poynting's theorem). The Poynting vector. Tensors.	8.1.1, 8.1.2	8-1--8-8
Friday 2/10	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. Field momentum and momentum conservation in electrodynamics (motivation).	8.2.1, 8.2.2	8-8--8-14
Tuesday 6/10	Tensors with rank > 2 (forgotten last time). Force density. The Maxwell stress tensor. Total force on charges inside a volume. Pressure and shear forces. Momentum density in EM fields. Conservation of momentum. Example: Maxwell stress tensor for two charged cylinders.	8.2.2, 8.2.3	8-15--8-20, 8-22--8-23	Example: Maxwell stress tensor for two charged cylinders
Friday 9/10	Example (continued). 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.	8.2.2, 8.2.4, 9.1.1, 9.1.2, 9.1.4, 9.2.1, 9.2.2	8-19, 8-26--8-27, 9-1--9-8
Tuesday 13/10	(Only 1 hour lecture, the 2nd hour was used for the numerical project.) Energy and momentum in EM waves in vacuum. Time-averaged quantities. Intensity. Radiation pressure. Averages of products expressed in the complex notation.	9.2.2, 9.2.3	9-8--9-13
Friday 16/10	EM waves in linear nonconducting media. Reflection and transmission at a flat interface between two such media. TM (p) and TE (s) linear polarization. Laws of reflection and refraction (Snell's law). Fresnel equations for p-polarization. Brewster's angle.	9.3.1, 9.3.3	9-14, 9-16--9-17, 9-27, 9-34
Tuesday 20/10	Intensities, reflection and transmission coefficients for p-polarization. Total internal reflection, s-polarization (very brief discussions). EM waves in conductors: Attenuation, skin depth, phase difference between E and B fields, complex dielectric function. Dispersion: wave shape distortion, phase velocity, group velocity.	9.3.3, 9.4.1, 9.4.3	9-42--9-44, 9-46--9-47
Friday 23/10	"Anomalous" dispersion. Guided waves. Optical fibers (total internal reflection). Hollow metallic wave guide. TE/TM/TEM waves. TE waves in rectangular wave guide. Scalar and vector potentials.	9.4.3, 9.5.1, 9.5.2, 10.1.1	9-46--9-47, 9-55--9-61, 10-1--10-3
Tuesday 27/10	Inhomogeneous wave equations for the potentials. Gauge transformations. The Coulomb and Lorenz gauges. Properties of the potentials in the Lorenz gauge, the retarded time. The Green function method. Green functions for the Laplacian and d'Alembertian operators.	10.1.1-10.1.3, 10.2.1	10-3--10-10, 10-13--10-15 ("note-02" about Green functions is also relevant)
Friday 30/10	Retarded and advanced Green functions, causality. The retarded potentials for arbitrary sources. The associated E- and B-fields (Jefimenko's equations). The (Lienard-Wiechert) potentials for a moving point charge. The associated E- and B-fields (started the derivation).	10.2.1, 10.2.2, 10.3.1, 10.3.2	10-16--10-17, 10-22--10-33
Tuesday 3/11	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. Electric dipole radiation.	10.3.2, 11.1.1, 11.1.2	10-33--10-34, 11-1--11-3, 11-9, 11-20
Friday 6/11	Electric dipole radiation. Magnetic dipole radiation (very brief discussion). Radiation from an arbitrary localized source.	11.1.2-11.1.4	11-9--11-15, 11-17
Tuesday 10/11	Lecture cancelled. The time between 11:15 and 12:00 was used for an extra tutorial hour.
Friday 13/11	Multipole expansion for the vector potential of an arbitrary localized source. The n=0 term: electric dipole radiation. The n=1 term: magnetic dipole and electric quadrupole radiation (very brief discussion). Radiation fields from a point charge.	11.1.4, 11.2.1	11-15--11-23, 11-26--11-27, 11-28--11-31
Tuesday 17/11	Radiation from a point charge. The Larmor formula and Lienard's relativistic generalization. Radiation reaction (very brief discussion). Special relativity (very brief discussion): Lorentz transformations. 4-vectors. Transformation properties of the E- and B-fields. End of new material, started repetition.	11.2.1, 11.2.2, 12.1.3, 12.1.4, 12.3.2-12.3.5	11-29--11-35
Friday 20/11	Repetition. A previous exam problem (brief discussion).