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Assume that the fields are NOT point-charge to point-charge. This is a classical concept that was born out of the experiments of Coulomb, Faraday and others around 175 odd years ago. The form of the inverse square followed Newton's gravitional law, and the experiments in electricity and magnetism are MACROSCOPIC; but we are interested in atoms say (to begin with). Looking at OTHER ways that people have dealt with such issues, and if you've done a masters thesis in axisymmetric antenna structures, you tend to learn a lot of good real world maths including some of the older techniques, Von Hippel, "dielectrics and waves" Wiley, 3rd printing, 1962, uses a rotating vector. He solves the problem of far-field radiation from a dipole antenna. In my phd (bioelectromagnetics), I studied this in regards a similar problem where it was desired to obtain ZERO RADIATION in the far-field. The way to do this is by adjusting components so that the RADIATION IN is equal to the RADIATION OUT (remember we are treating the field as ubiquitous and infinite, which turns out to be incorrect, but for this case there's heaps of energy residing IN the field, stored in the infinite field).

So we CAN in fact have zero radiation antennas; this leads to a realisation of exactly what is an 'imaginary' field and what it means physically. the antenna structure needs to be a cross dipole where there is a phase difference of pi/2 (or "j" between the ttwo dipoles. This is NOT an electric dipole but a ring dipole, a magnetic dipole. and so we have two toriods which have to 'access' each other, so most conveniently we have a solid sphere of metal in which two oscillating fields are established (no mean feat, but nice theoretically)-so much for lecture 1!! see you tomorrow