10. Potentials and Fields Introduction of potential V substantially simplifies finding solutions of problems in Electrostatics. Does such a simplification.

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Presentation transcript:

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

Gauge Transformations

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

Equations for the retarded potentials Inhomogeneous wave equations.

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

Circular wavefronts diverging from a point Source in a ripple tank. 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.

Green’s Function Very short and intense pulse:

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

Infinite straight wire

Change of variables in a volume integral

Moving point charge

Lienard-Wiechert potentials

Point charge at constant velocity

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

Point charge at constant velocity