Electrodynamics - Physics 642 Manuel Berrondo

(design by Tim Wendler, Dan Jensen, and Felipe Rivera)

Books

Textbook: Electrodynamics by Fulvio Melia

Reference book: Classical Electrodynamics by John D. Jackson

Homework problems from Jackson

Notes on Geometric Algebras by Manuel Berrondo - online

Overview of E&M

1. Electromagnetic Fields given the sources

Maxwell's Equation(s) (homogeneous and

inhomogeneous)

Time independent sources

Electrostatics

Magnetostatics

Wave propagation

in vacuum

in matter

o reflection

o refraction

o polarization

with boundary conditions

o wave guides

o cavities

2. Electromagnetic Radiation

Radiation fields

Sources of Radiation

Dispersion

Scattering of electromagnetic fields

3. Motion of Charges: charge and current

distributions

Lorentz force

non-relativistic (Newton)

non-relativistic E & M

relativistic

Relativistic mechanics

Lorentz group of transformations

4. Radiation from Point Sources

Liénard-Wiechert potentials

Liénard-Wiechert fields

Accelerated charges

5. Coupling Maxwell and Lorentz

Plasmas and magneto-hydrodynamics (MHD)

(distributions)

Point particles

Lorentz-Dirac equation

Unsolved features

6. Formal Aspects

Vector integral theorems

integration in 3-d

“” (proper vectors) notation

Clifford algebras

Pauli G3

Dirac G 1,3

Green's functions

in 3d, 4d

(r, t) domain

(k, ) domain

Dispersion relations

Conservation theorems

Poynting

Maxwell tensor

Lagrangian formulation of fields

Review

1. Green’s functions

Linear operator L; solve inhomogeneous eqn.

In n-d configuration space x :

where

Dirac’s delta distribution acts as unit w.r. to

convolution *:

Poisson eq. in 3-d:

with

In r-space:

Defining

the solution is:

For ,

In 4-d, account for retardation (speed c)

Retarded Green’s function:

Advanced Green’s function:

Using the light cone:

Retarded solution:

2. Maxwell’s equations (Gaussian units)

In integral form:

3. Boundary Conditions

4. Units

SI Gaussian

ε0 1/4π

0 c 4π/c

cB B

cA A

v x B v x B/c

5. Potentials

Gauge transformations:

6. Conservation laws

Charge:

Energy:

energy density

Poynting vector: