1. §7.2 Maxwell Equations the wave equation
Christopher Crawford
PHY 311

2. Final Exam Based on 5 formulations of electromagnetism
Derivative chain – gauge, potentials, fields, sources
Structure of and relations between different formulations
Field calculation methods organized around formulations
Cumulative – uniform weighting through whole semester
Will be 50% longer than midterm exams
Similar problems as midterms
Essay question – structure of EM fields / media
Proof – relation between formulations
Integration – Coulomb / Biot-Savart / Potential
Integral – Gauss / Ampère [or modified versions]
Boundary value problem – see examples
Components – capacitor, resistor, inductor

3. Outline
Review – electromagnetic potential & displacement current propagate electromagnetic waves
Capacitive ‘tension’ vs. inductive ‘inertia’
Unification of E and B – filling in the cracks
Derivative chain – different representations of fields
Wave equation and solution – Green’s fn. and eigenfn’s

4. Electromagnetic Waves
Sloshing back and forth between electric and magnetic energy
Interplay: Faraday’s EMF  Maxwell’s displacement current
Displacement current (like a spring) – converts E into B
EMF induction (like a mass) – converts B into E
Two material constants  two wave properties

5. Review: Two separate formulations
ELECTROSTATICS
Coulomb’s law
MAGNETOSTATICS
Ampère’s law
E+B: Faraday’s law; b) rho + J: conservation of charge; c) space + time

6. Review: One unified formulation
ELECTROMAGNETISM
Faraday’s law stitches the two formulations together in space and time
Previous hint: continuity equation

7. Unification of E and B
Projections of electromagnetic field in space and time
That is the reason for the twisted symmetry in field equations

8. Unification of D and H
Summary

9. Wave equation: potentials

10. Wave equation: gauge

11. Wave equation: fields

12. Wave equation: summary
d’Alembert operator (4-d version of Laplacian)

13. Homogenous solution
Separate time variable to obtain Helmholtz equation
General solution for wave Boundary Value Problems

14. Particular solution Green’s function of d’Alembertian
Wikipedia: Green’s functions