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.
Jean le Rond d'Alembert Siméon Denis Poisson Pierre ‐ Simon Laplace
Legendre Polynomials Solutions to the Legendre Equation 2 d y d y 2 (1 x ) 2 x l l ( 1) y 0 2 d x d x Expressed compactly by Rodregues’ Formula Orthogonality:
Dipole Field Lines
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