For the total density of energy-flow (
) we must of course add to the above the components of the Poynting vector. Writing as usual
and
for the electric and magnetic force intensities and calling (
) the velocity of light, we have
|
(2)
|
These equations give the density of the total energy-flow through any purely electrical system, in which the ordinary electrical laws hold universally.
6. Consider an isolated electrical system moving as a whole through space with the constant velocity (
). A constant velocity will be possible if the system retains on the average the same internal structure. The total average rate of transfer of energy corresponding to the movement of such a system is evidently (
), where
is the total contained energy. Another expression for the same thing is to be obtained by integrating throughout the system the components along (
of
) given in equations (2). In order that the velocity (
) may appear explicitly, however, it is necessary that the velocity (
), which was used in equations (2), be written as the sum of (
) and another velocity (
). Then (
) is the velocity with respect to axes moving with the system.
If
are the direction cosines of the constant velocity (
), we have for the total energy-flow (
) in the direction of (
),
|
(3)
|