M. Fabbrichesi , SISSA

Radiation from an oscillating charge distribution

In the begining of this lesson, corrections to the potentials Φ and A are derived leading to the so-called retarded potentials ( Liénard-Wiechert potentials ) where it is taken into account that a signal takes a finite time, corresponding to the velocity of light, to propagate from the source point of the field to the observation point r. Next, the problem of the radiation from an oscillating charge distribution is considered. Solutions for the vector potential are found for both the near zone and far zone. For the latter it is shown that the leading term of the vector potential depends on the electric dipole moment p. Expressions for the fields E,H and for the power radiated per unit solid angle are then given [Jackson, sec. 14.3]. In the last part of the lesson it is shown how by starting from the definition of dipole and by using the Liénard-Wiechert potentials it is possible to come to the result previously found for the radiated power (Hertz oscillator).