Note 1. The fundamental electro-magnetic equations of Maxwell for stationary media are:—
curl H = 1/c ([part]D/[part]t + ρν) (1)
curl E = -1/c [part]B/?]t (2)
div D = ρ B = μH
div B = ο D = k?]E
According to Hertz and Heaviside, these require modification in the case of moving bodies.
Now it is known that due to motion alone there is a change in a vector R given by
([part]R/[part]t) due to motion = u. div R + curl [Ru]
where u is the vector velocity of the moving body and [Ru] the vector product of R and u.
Hence equations (1) and (2) become
c
curl H = [part]D/[part]t + u div D + curl Vect. [Du] + ρν (1·1)
and
-c curl E = [part]B/[part]t + u div B + curl Vect. [Bu] (2·1)
which gives finally, for ρ = ο and div B = O,
[part]D/[part]t + u div D = c curl (H - 1/c Vect. [Du]) (1·2)
[part]B/[part]t = -c curl (E - 1/c Vect. [uB]) (2·2)
