Electromagnetic Reverberation Chambers

Appendix 5

Electric Dipole Formulas

A5.1. Complete formulas of the electric dipole

Let us consider a short wire of longitudinal dimension ΔL where a uniform and sine wave current I of ω angular frequency flows. An observer P is located at a distance r from the short wire in order to meet the r >> ΔL condition (Fresnel region).

With the assumptions previously established and taking into account the fact that the distance r is attached to a spherical coordinate system, whose origin coincides with the center of the wire, it is an electric dipole, which is represented with the notation conventions from Figure A5.1. Solving the wave equation in order to determine the radiated electromagnetic fields from this electric dipole, leads to an electric field vector, including two projections according to the polar angle and θ the radial direction r respectively. A magnetic field vector with symmetry of revolution including only one component is attached to the previous electric field vector. The magnetic field vector is directed according to the azimuth angle φ [DEM 05]:

[A5.1]

We find, in this relation, unit vectors which were omitted in Figure A5.1.

Figure A5.1. The electric dipole in the ...