Electric and magnetic fields 1

Classical Mechanics (Fall, 2011)

November 21, 2011

This lecture introduces the static electric and magnetic fields, the associated Lagrangian and the Lorentz force. The vector potential, it's gauge field and gauge invariance are also introduced.

  • Magnetic and electric fields
  • The concept of field
  • The “del” or “nabla” symbol
  • Vector calculus: Gradient, Divergence and Curl
  • The Levi-Civita symbol
  • Algebra: div curl and curl grad vanish
  • The vector potential and why it's needed
  • Gauge field: "Gauge" is a misnomer
  • Lorentz force. Lorentz force compared with the Coriolis force
  • Lagrangian for charged particles in a electro-static and magneto-static fields
  • Gauge invariance of the equations of motions associated to the electro-magneto-static Lagrangian