There seems to be quite a few people in this newsgroup who, when they
can, keep bringing up the subject of E and B not causing one another,
contrary to what is outlined in most text books. That Jefimenko was
the first to see this, via his equations which express E and B in
terms of their sources at retarded time t'. E and B are functions of
the charge density Rho(r', t'), d/dt Rho(r', t'), current density
J(r', t'), d/dt J((r', t'), and R
where R = r - r', retarded time t' = t - R/c, r is the field point at
time t, r' is the position of the source at time t':
http://en.wikipedia.org/wiki/Jefimenko's_equations
On the other hand, the Lienard-Wiechert equations were derived over
100 years ago and, in my view, go further by exploiting the fact that
most EM problems consist of charge moving continuously through space.
The equations thus end up vastly simplified giving E and B just in
terms of the position of the charge and observation point; velocity
and acceleration of the moving charge:
E_ = e[ (n_ - B_)( 1 - B^2) / k^3R^2 + n_ x (( n_ - B_) x a_) /
c^2K^3R
B_ = [_n] X E_
Where:
e = charge on moving source
c = speed of light
_ is a vector
R_ is the position vector from where the charge was to the field point
n_ = R_/R,
_B = u_/ c
K = 1 - B_ dot n_
I don't see any advantages to using Jefimenko's over those of Lienard-
Wiechert and would be interested in your views.
Cheers.
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