Electrodynamics

physics

Mathematical analysis in multi-dimensions, vector calculus. Lagrangian formulation of classical mechanics.

Classroom

Good knowledge of classical electrodynamics is necessary for understanding most of the phenomena encountered in every-day life.

It is also required for further studies of advanced topics, like quantum theory of fundamental interactions. Methods of electrodynamics are universal and widely applied in all domains of modern physics.

Electromagnetic interactions together with weak and strong interactions form presently the Standard Model of particle physics which has been tested and confirmed with remarkable precision. Electrodynamics is the best understood part of this model. The formulation of classical electrodynamic in the second half of XIXth century started the process of unifying all fundamental forces with the recognition, that electric and magnetic forces are two incarnations of a single fundamental interaction.

Good working knowledge of electrodynamics is necessary for understanding of modern quantum theory of fundamental interactions.

The goal of the lecture is to present a complete and consistent description of electromagnetic phenomena and to formulate basic theoretical ideas and technical tools.

Program:

1. Maxwell equations in vacuum, their invariance under Lorentz transformations, properties and implications, conservation laws.

2. Elements of the special theory of relativity: addition of velocities, spacetime and four-tensors, covariant formulation of Maxwell equations.

3. Maxwell equations in matter, macroscopic fields, boundary conditions.

4. Electrostatics and magnetostatics: basic equations, Dirichlet and Neumann boundary conditions, Green functions, multipole expansions.

5. Non-stationary electromagnetic field: electromagnetic waves in vacuum and in matter, field of a moving charge, electromagnetic radiation.

These topics will be discussed in the order chosen by the lecturer, not necessarily conforming to the ordering above.

A minimal amount of time needed to pass successfully include:

- 90h of student's participation in lectures and classes

- 70h for homework

- 20h for preparation to written and oral exams

Prepared by Wojciech Satuła, November 2011 (modified by Janusz Rosiek, 2014)

Textbooks:

1. D. J. Griffiths, Introduction to electrodynamics - basic textbook

2. J. D. Jackson, Classical electrodynamics

3. M. Suffczyński, Elektrodynamika

4. L. Landau, E. Lifszyc, Elektrodynamika ośrodków ciągłych

5. L. Landau, E. Lifszyc, Classical field theory

Problems:

6. W. Batygin, I. Toptygin, Zbiór zadań z elektrodynamiki

7. M. Zahn, Pole elektromagnetyczne

8. L. Grieczko i in., Zadania z fizyki teoretycznej

9. Problems from the above textbooks.

Knowledge:

Knows Maxwell's equations in vacuum and in matter, as well as the boundary conditions at the interfaces of media.

Has basic knowledge of special relativity and its mathematical structures. Understands that classical electrodynamics is a relativistic theory and comprehends the implications of this fact.

Knows the conservation laws of charge, energy, and momentum, and understands new concepts related to these, such as the Poynting vector, field momentum, and Maxwell's stress tensor.

Has basic knowledge of electromagnetic fields in vacuum and in media, the laws of refraction and reflection, and is familiar with Fresnel's laws.

Understands the issues of light absorption in a conducting medium.

Has knowledge of radiation fields generated by moving charges, particularly by monochromatic oscillating sources.

Skills:

Can solve Maxwell's equations with given boundary conditions. Can utilize a wide range of theoretical methods, from the method of images and the method of orthogonal polynomials (special functions) to Green's functions and conformal transformations. Can formulate Maxwell's laws in a relativistically invariant manner. Can solve time-dependent problems, particularly able to calculate the radiation power distribution generated by monochromatic sources.

Attitudes:

Is willing to formulate and communicate opinions on fundamental issues in electricity and magnetism. Understands the need to popularize knowledge.

Midterm exams and written final exam. In order to be admitted to the l

exam students are obliged to obtain a score at least 50% from the sum of points from the midterm exams.

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