1. Electromagnetic Field Equations (8 lectures) Maxwell's equations - - PowerPoint PPT Presentation

• 1. Electromagnetic Field Equations (8 lectures)

Maxwell's equations and wave solutions. Definition of scalar and vector potential. Poisson's equation and electro‐ and magnetostatics; multipole expansions. Electrodynamics in Lorentz Gauge; the inhomogeneous wave equation and the retarded time.

• 2. Accelerating Charges (6 lectures)

Lienard‐Wiechert potentials; Power radiated from an arbitrarily moving charge. Larmor's power formula; synchrotron radiation; bremsstrahlung.

• 3. Harmonically Varying Sources (2 lectures)

Multipole radiation: electric (Hertzian) and magnetic dipole radiation; slow‐down of

• pulsars. Rayleigh and Thomson scattering.
• 4. Electromagnetism and Relativity (8 lectures)

Four vectors and tensors; Covariant and contravariant formalism of Lorentz transformations; relativistic dynamics. Consistency of Maxwell's equations and relativity. Electromagnetic field tensor and electrodynamics in covariant form.

Pierre‐Simon Laplace Siméon Denis Poisson Jean le Rond d'Alembert

Solutions to the Legendre Equation Expressed compactly by Rodregues’ Formula Orthogonality:

Legendre Polynomials

2 2 2

d d (1 ) 2 ( 1) d d y y x x l l y x x     

Dipole Field Lines