# Classical Electrodynamics

### 13

### Lessons

### 13

### Videos

### EM

### PREREQUISITE

### 2h:30m

### Duration

### English

### Language

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### Overview

Formulation of the electromagnetism theory is an essential key to our understanding of nature, such as classical optics, microwaves and electric circuits. Both electric and magnetic forces were discovered millennia ago prior to being formulated by Coulomb and Bio-Savart. However, Maxwell showed that electric and magnetic fields are both generated and altered by each other. This revolutionary discovery led to a novel and unique branch of physics, named electrodynamics. In this course, we review several important concepts in the Classical Electrodynamics, among the others, such as Green’s functions, boundary-value problems, multipoles expansions, electrostatic of macroscopic media, magnetostatics, time-varying fields, Maxwell’s equations and gauge transformations, and covariant formulation of classical electromagnetism.

### COMPLETING THIS COURSE WILL HELP YOU:

- Electrostatic and boundary-value problems
- Green functions and determining electrostatic under different conditions
- Multipoles expansions and electrostatics of Macroscopic Media
- Gauges and Maxwell's equations

### Who is the course for?

This course is suitable for physics graduate students that are familiar with electromagnetism. In the current form, Electrodynamics has been developed over the last 150 years, and thus, it is impossible to learn all these developments historically. Therefore, the contents are chosen selectively for the graduate programme by the faculty of science. Note that propagation of EM fields, radiation, and scattering will not cover during this semester.

### MAIN TEXTBOOK

The course will be based on *Classical Electrodynamics* (3rd Edition) by *John David Jackson* (who is a Canadian–American physicist born in London-Ontario). Chapters 1, 2, 3, 4, 5, 6, and 11 of the book will be covered in the winter semester.

### Learning Path

Introducing Coulomb’s law, Electric field, SI and CGS units, Delta Functions, Electrostatic Energy, Gauss and Stokes laws and field continuity at boundaries.

**Video 2h:30m NOTE (PDF) **

Introducing Green theorems, Green functions, Dirichlet, Neumann, and Cauchy boundary conditions.

**Video 2h:24m NOTE (PDF) **

Dirichlet and Neumann boundary-value problems, Image charge technique, and finding potentials for simple boundary conditions.

**Video 2h:11m NOTE (PDF) **

Dirichlet and Neumann boundary-value problems, Image charge technique, and finding potentials for simple boundary conditions.

**Video 2h:20m NOTE (PDF) **

Special functions, Legendre polynomials, sinusoidal function, and a few application examples.

**Video 1h:40m NOTE (PDF) **

Laplacian in the cylindrical and spherical coordinates, Bessel functions and Legendre polynomials.

**Video 2h:22m NOTE (PDF) **

Solving Laplacian in the spherical coordinates, introducing Legendre polynomials/functions, Spherical Harmonics and solving a few examples.

**Video 2h:17m NOTE (PDF) **

Expanding potential in the Cartesian and Spherical coordinates in terms of the monopole, dipole, quadrupole, etc.

**Video 2h:17m NOTE (PDF) **

Introducing the dipole approximation; calculating energy of specific charge distribution in an arbitrary electric field; dipole moment density, polarisation and dielectric.

**Video 2h:17m NOTE (PDF) **

Introducing polarisation and dielectric constant, electric field at boundary of different dielectrics, and solving Dirichlet boundary conditions.

**Video 2h:17m NOTE (PDF) **

Introducing magnetic flux density vector, Biot-Savart and Faraday’s laws, driving differential equation for magnetic flux density and vector potential; Finding vector potential and magnetic flux density for specific geometries.

**Video 2h:17m NOTE (PDF) **

Introducing magnetic flux density vector inside materials, introducing magnetization, magnetic dipole moment, and scalar magnetic potential.

**Video 2h:17m NOTE (PDF) **