Electric and magnetic fields 2

Classical Mechanics (Fall, 2011)

Lecture Playlist

  1. State diagrams and the nature of physical laws

  2. Newton's law, phase space, momentum and energy

  3. Lagrangian, least action, Euler-Lagrange equations

  4. Symmetry and conservation laws

  5. The Hamiltonian

  6. Hamilton's equations

  7. Liouville s theorem

  8. Poisson brackets

  9. Electric and magnetic fields 1

  10. Electric and magnetic fields 2

November 28, 2011

This final lecture is a general review of all the concepts learned so far applied to a particle in electric and magnetic static fields.

Topics: 
  • Review of the vector potential, concept of gauge and gauge invariance
  • Lorentz force law
  • Example of different vector potentials for a constant magnetic field and the gauge transformation that relate them
  • Importance of gauge invariance and choice of gauge
  • Lagrangian of a particle in a static magnetic field. Review of the related action gauge invariance
  • Distinction between mechanical and canonical momentum: only the canonical momentum is related to symmetries and invariance
  • Derivation of the Euler-Lagrange equation of motion from the magneto-static Lagrangian and rediscovery of the Lorentz force
  • Justification of the vector potential as an essential tool for the least action principle
  • Derivation of the magneto-static Hamiltonian
  • Smart choice of gauge and derivation of the Lorentz force from symmetry arguments only, “cyclic coordinates”
  • Circular motion of a charged particle in a static magnetic field
  • Monopoles discussion as part of the questions session
  • Brief Quaternions discussion as part of the questions session
References