Electromagnetic field produced by an oscillating electrical dipole

ELECTROMAGNETIC FIELD PRODUCED BY AN OSCILLATING ELECTRICAL DIPOLE 

Let D(t) = D e to be the electrical moment of an oscillating dipole located at the origin of the co-ordinates. For instance, this moment could be created by applying an external field 0(t) to a small dielectric object of polarizability a, located in 0 

We want to show that the electric field and the magnetic field produced at a point of position vector r are given, for large values of r, by the following expressions 

To find this result, we have only to calculate the vector potential A(r, t) and the potential V(r, t) corresponding to these fields, since 

The potential and the vector potential are related to the current j(r, t) and to the charge density p(r,t) by the equations 

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