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10. Potentials and Fields

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  1. 10. Potentials and Fields Introduction of potential V substantially simplifies finding solutions of problems in Electrostatics. Does such a simplification exist for Electrodynamics as well? Yes, it does: The retarded potentials

  2. Gauge Transformations

  3. Coulomb Gauge Used in electro- and magnetostatics Lorentz Gauge Used in electrodynamics Will be used further on.

  4. Equations for the retarded potentials Inhomogeneous wave equations.

  5. Spherical waves Another, very common solution of the wave equation: Example: sinusoidal spherical wave

  6. Sound waves from a telephone hand set spreading out in air. The waves have been made visible by sweeping out the space in front of the hand set with a light source whose brightness is controlled by a microphone. Circular wavefronts diverging from a point Source in a ripple tank.

  7. Green’s Function Very short and intense pulse:

  8. Be careful, the retarded time introduces a new and complicated dependence of Retarded Potentials

  9. Infinite straight wire

  10. Change of variables in a volume integral

  11. Moving point charge

  12. Lienard-Wiechert potentials

  13. Point charge at constant velocity

  14. The field of a moving point charge field attached to the charge radiated EM wave

  15. Point charge at constant velocity

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