1. Christopher Crawford PHY 311 2014-04-28
§7.2 Maxwell Equations
Christopher Crawford
PHY 311

2. Outline Review – TWO separate derivative chains (in space only)
ES and MS formulations: potentials and Poisson’s equation
THREE observations: a) Coulomb, b) Ampere, c) Faraday the third ties the derivative chains of the other two together
TWO cracks in the foundation – patching up space and time
Scalar potential, Maxwell’s displacement current
Example: potential momentum associated with a B-field
Example: the displacement current through a capacitor
Materials: THREE charges and FIVE currents
Maxwell Equations – unified symmetry in space and time
Differential & integral fields, potentials, boundary cond’s
Space-time symmetry – ONE complete derivative chain
Duality rotations – magnetic monopoles revisited

3. Two separate formulations
ELECTROSTATICS
Coulomb’s law
MAGNETOSTATICS
Ampère’s law

4. Two separate formulations
ELECTROSTATICS
MAGNETOSTATICS
Faraday’s law stitches the two formulations together in space and time

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

6. 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

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

8. Example: potential momentum

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

10. Maxwell’s equations Field equations
Boundary conditions: integrate Maxwell Eq.’s across surface

11. Electrical properties of materials
Same old THREE charges
Now: FIVE currents, include displacement!

12. Duality rotation