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Science Forum Index » Physics - Electromagnetic Forum » Jefimenko's versus Linenard-Wiechert equations...
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| blackhead... |
 Posted: Sat Jun 28, 2008 8:57 am |
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Guest
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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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| Benj... |
| Posted: Sat Jun 28, 2008 7:15 pm |
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Guest
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On Jun 28, 2:57 pm, blackhead <larryhar... at (no spam) softhome.net> wrote:
Quote: 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.
I don't see any advantages to using Jefimenko's over those of Lienard-
Wiechert and would be interested in your views.
What is this? A "contest" to determine who has the "best" equations?
Hey, they are equations! That means NONE are "best"!
The point is that when you start talking about equations (all of which
are derived from the same basic sources) they basically are "best"
when they provide the easiest answer to the particular problems you
are trying to deal with. Maxwell's equations maybe "wrong" in that
they are not causal, but on the other hand they have nevertheless
provided a huge library of practical EM answers that are reasonably
accurate. Jefimenko on the other hand deals with causality and
"retarded" potentials which are obviously the way the world works but
adds a level of complexity that is usually ignored when seeking
practical answers...UNLESS causality plays a crucial role in the
problems you are dealing with. The L-W potential approach has often in
the past been regarded as a mere mathematical trick, but there is more
to it than that. First off they do correctly assign causality for
retarded potentials (Jefimenko talks quite a bit about this). And even
more important, it appears the quantities like the vector magnetic
potential are more "fundamental" than the EM fields. The Aharonov-Bohm
solenoid effect indicates the more fundamental nature of A over B. But
on the other hand ALL these equations are "classical" and (even L-W)
quickly fail at the quantum level.
The bottom line is that none of these equations is "best" and each are
useful for certain problems and understandings. |
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| maxwell... |
| Posted: Sun Jun 29, 2008 11:47 am |
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Guest
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On Jun 28, 11:57 am, blackhead <larryhar... at (no spam) softhome.net> wrote:
Quote: 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.
See my response on June 29 in another thread:
http://groups.google.com/group/sci.physics.electromag/browse_frm/thread/43457040bd467476?hl=en |
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| Bill Miller... |
| Posted: Mon Jun 30, 2008 11:49 am |
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Guest
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"blackhead" <larryharson at (no spam) softhome.net> wrote in message
news:dcf5289b-d496-4929-a447-a0b312a8e916 at (no spam) z72g2000hsb.googlegroups.com...
Quote: 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.
THIS is the problem! Maxwell's equations are not (and cannot be) causal
since they represent entities that occur simultaneously. The basic idea
behind causality is very simple: A cause MUST PRECEDE an effect.
As you stated above, most textbooks teach that E causes H and vice versa.
THAT -- as I mentioned in another thread -- has caused any number of
researchers, engineers and business people to spend large amounts of time
and MONEY. The waste occurred in trying to build devices to *use* the
non-existent ability of an E field to generate an H field!
Quote: That Jefimenko was
the first to see this,
Actually, it looks like Panofsky was the first to express E and H in terms
of retardation and charges. I don't know if Jefimenko developed his
equations without knowing of Panofsky's work (he does not reference Panofsky
anywhere) but it appears that they both arrived at the same basic equations
via different procedures.
Quote: 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.
In my opinion, the primary advantage to Jefimenko's approach lies not in the
simplicity (or lack thereof) of the equations. It lies instead in the
logical -- and rigorous -- manner that he uses the basic idea of causality.
Bill |
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