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

2. Outline
Review – electromagnetic potential & displacement current consequences of Faraday law and conservation of charge
Physical interpretation – unified symmetry in space and time
Displacement current – capacitor
Electromagnetic momentum – inductor
Electromagnetic waves – oscillation of energy between the 2
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

3. 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

4. TWO cracks in the foundation
Faraday’s law appears to violate conservation of energy?
Unified gauge transformation for V and A
Continuity equation vs. Ampère’s law

5. Example: current through a capacitor
Which surface should one use for Ampère’s law?

6. Example 7.8: potential momentum
Angular momentum from turning off the field
Potential momentum associated with the field
Magnetic field energy acts as “electromagnetic inertia”

7. Magnetic field energy
Work against the “back-EMF” is stored in the magnetic field
It acts as “electrical inertia” to keep current moving

8. 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

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

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

11. Unification of D and H
Summary