by TANG MUOI
It is shown that the distribution of electromagnetic energy of a stationary
current in a three-dimensional conducting medium can be readily computed
when the latter is a half space containing a finite number of 
centers
of harmonic conductivity.
The density of electric energy in the lower half-space is easily obtained owing
to the finiteness of the formulae for the electric fields in the – media.
In the upper half-space (air) we use the Poisson integral to extend analytically
the electric potential whose values are known on the surface of the ground.
We notice the existence of an important discontinuity of the density of electric
energy at the ground surface, due to the persistence of a nonzero vertical
component of the electric field in the air down to the ground.
As far as the magnetic energy is concerned, we first perform the computation
in the upper half-space; here the magnetic field can be obtained by an analytic
continuation of the vertical magnetic component off the ground surface, where
it can be expressed in finite terms. A simple lemma allows then one to deduce
the magnetic field in the lower half space from the one already known in the
upper half space.
Several graphs for the distribution of the electric and magnetic energy density
in an medium
containing two harmonic centers in the lower half space illustrate the way
in which our results may be applied and point out the influence that
conducting regions may exert upon these distributions both inside the ground
and in the air.