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

4. Gauge Transformations

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

6. Equations for the retarded potentials Inhomogeneous wave equations.

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

8. 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.

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

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

11. Infinite straight wire

13. Change of variables in a volume integral

14. Moving point charge

15. Lienard-Wiechert potentials

16. Point charge at constant velocity

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

18. Point charge at constant velocity