Classical Electrodynamics

A rigorous Jackson-level graduate treatment of classical electrodynamics—from electrostatics and multipole expansions through Maxwell's equations, electromagnetic waves, radiation theory, and the relativistic formulation of electrodynamics.

Course Overview

Classical electrodynamics is one of the most beautiful and complete theories in physics. Maxwell's unification of electricity, magnetism, and optics into four compact equations stands as one of the greatest intellectual achievements in science. This course follows the graduate-level treatment in the tradition of Jackson, covering the full mathematical structure from electrostatics through relativistic electrodynamics.

What You'll Learn

  • • Electrostatics: fields, potentials, boundary value problems
  • • Multipole expansions and Green's function methods
  • • Magnetostatics, magnetic materials, and induction
  • • Maxwell's equations in differential and integral form
  • • Electromagnetic waves: propagation, reflection, waveguides
  • • Radiation from accelerating charges and antennas
  • • Scattering and diffraction of EM waves
  • • Special relativity and covariant electrodynamics

Prerequisites

• Multivariable calculus and vector calculus• Ordinary and partial differential equations• Linear algebra• Classical mechanics

• Undergraduate electromagnetism

• Special relativity (for Part IV)

• Complex analysis (helpful)

References

  • • J. D. Jackson, Classical Electrodynamics (3rd ed.)
  • • D. J. Griffiths, Introduction to Electrodynamics (4th ed.)
  • • A. Zangwill, Modern Electrodynamics
  • • L. D. Landau & E. M. Lifshitz, Classical Theory of Fields

Course Structure

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Part I: Electrostatics

Electrostatics review, multipole expansion, boundary value problems, and dielectrics.

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Part II: Magnetostatics & Induction

Magnetostatics, magnetic materials, electromagnetic induction, and Maxwell's equations.

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Part III: EM Waves & Radiation

Electromagnetic waves, waveguides and cavities, radiation and antennas, scattering and diffraction.

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Part IV: Relativistic ED

Special relativity and EM, relativistic particles, radiation reaction, and EM in media.

Key Equations

Coulomb's Law

$$\mathbf{F} = \frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{r^2} \hat{r}$$

Force between two point charges separated by distance r

Laplace Equation

$$\nabla^2 \Phi = 0$$

Governs the potential in charge-free regions

Multipole Expansion

$$\Phi(\mathbf{r}) = \frac{1}{4\pi\epsilon_0} \sum_{l=0}^{\infty} \frac{1}{r^{l+1}} \int (r')^l P_l(\cos\theta') \rho(\mathbf{r}') \, d^3r'$$

Expansion of potential in terms of Legendre polynomials

Maxwell's Equations

$$\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}, \quad \nabla \cdot \mathbf{B} = 0$$$$\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}, \quad \nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \mu_0\epsilon_0 \frac{\partial \mathbf{E}}{\partial t}$$

The complete set governing all classical EM phenomena

Wave Equation

$$\nabla^2 \mathbf{E} - \mu_0\epsilon_0 \frac{\partial^2 \mathbf{E}}{\partial t^2} = 0$$

Derived from Maxwell's equations in vacuum

Liénard-Wiechert Potentials

$$\Phi = \frac{q}{4\pi\epsilon_0} \frac{1}{R(1 - \hat{R}\cdot\boldsymbol{\beta})}\bigg|_{\text{ret}}$$

Retarded potentials for a moving point charge