Re: 1 FERTZ

From: Y.Porat (maporat_at_012.net.il)
Date: 06/02/04 

Date: 2 Jun 2004 08:59:13 -0700

Bjoern Feuerbacher <feuerbac@thphys.uni-heidelberg.de> wrote in message news:<c9k5iv$hn$1@news.urz.uni-heidelberg.de>...
> Y.Porat wrote:
> > Bjoern Feuerbacher <feuerbac@thphys.uni-heidelberg.de> wrote in message news:<c9hgus$pr5$1@news.urz.uni-heidelberg.de>...
> >
> >>Y.Porat wrote:
> >>
> >>>Bjoern Feuerbacher <feuerbac@thphys.uni-heidelberg.de> wrote in message ne
> >>>
> >>>>
> >>>>
> >>>>>------------------
> >>>>>because *you are unable to do it crook!!!
> >>>>
> >>>>For the 30th time: according to Maxwell's equations, a multipole moment
> >>>>which is changing periodicaly with a frequency f will produce an em wave
> >>>>with that same frequency f. That was proved more than 100 years ago.
> >>>
> >>>------------------
> >
> > we are not interested in your 'explanations'
> > we are interested in your *calculations*- crook
>
> The calculation I referred to above can be found in any textbook. But
> since you *insist*, I will reproduce it here (and you won't understand
> anything about it and will call it "obfuscation"...).
>
> This will get a bit long, but you insisted... I won't give all of the
> tiny steps in between - if you want to see those, too, you can look them
> up in any book on electrodynamics. Most of them even can be found in
> books on vector calculus.
>
>
> Start with Maxwell's third equation:
> div B = 0 (1)
> Keep in mind that B and E are vector fields, and please notice that I
> am working in Gaussian units! Also, I only give the derivation for a
> charge density and current density in a vacuum (after all, the earth
> moves through a vacuum!); the derivation for other media would be similar.
>
> This implies that there exists a vector field A (called the "vector
> potential") so that
> B = rot A (2)
> Now take the second equation:
> rot E = - 1/c del B / del t (3)
> (the "del's" imply here a partial derivative)
>
> Insert (2) into (3) and rearrange the formula:
> rot(E + 1/c del A / del t) = 0
>
> This implies that there exists a scalar field Phi (called the "scalar
> potential" or simply "potential") so that
> E + 1/c del A / del t = - grad Phi (4)
>
> Now take the first equation:
> div E = 4 pi rho
> and the fourth:
> rot B = 4 pi/c j + 1/c del E / del t
> rho is here the charge density (a scalar field) and j is the current
> density (a vector field)
>
> Insert (2) and (4) here and rearrange the equations a bit; the results are:
> (1/c^2 del^2/del t^2 - Del) Phi - 1/c del/del t (div A + 1/c del Phi/del
> t) = 4 pi rho (5)
> and
> (1/c^2 del^2/del t^2 - Del) A + grad (div A + 1/c del Phi/del t)
> = 4 pi/c j. (6)
> I use "Del" here to denote the Laplace operator.
>
> Phi and A are not uniquely defined; one can make a so-called "gauge
> transformation" without changing E and B. I.e. one can use
> Phi ' = Phi + 1/c del/del t Lambda
> and
> A' = A - grad Lambda
> instead of Phi and A, with an arbitrary function Lambda. One can use
> this gauge freedom to simplify the equations (5) and (6) above ("gauge
> fixing"); one gauge condition which is commonly used is the "Lorentz gauge":
> div A + 1/c del Phi/del t = 0
>
> So the equations (5) and (6) simplify to:
> (1/c^2 del^2/del t^2 - Del) Phi = 4 pi rho
> and
> (1/c^2 del^2/del t^2 - Del) A = 4 pi/c j.
>
> Now these differential equations can be solved with the help of the
> so-called "retarted Green's function" (one could also use the "advanced
> Green's function" or linear combinations of the two, but for emission
> of radiation, the retarted Green's function is the relevant one). One
> then gets the "retarted potentials":
> Phi(r,t) = int dV' rho(r, t - |r-r'|/c) / |r-r'| (7)
> and
> A(r,t) = 1/c int dV' j(r, t - |r-r'|/c) / |r-r'| (8)
> The integral here runs over the whole volume, r and r' are vectors, and
> the combination t - |r-r'|/c is called the "retarted time".
>
> So far, the derivation has been completely general. Now we come to
> charge and current densities which change periodically:
> rho(r,t) = rho_0(r) e^(-i omega t) (9)
> and
> j(r,t) = j_0(r) e^(-i omega t) (10)
> (please notice that rho_0 and j_0 are not entirely arbitrary - they obey
> the continuity equation). omega here is the "circular frequency"; it is
> simply an abbreviation for 2 pi f, where f is the frequency.
>
> Insert (9) and (10) into (7) and (8) and rearrange the equations a
> bit; then one gets:
> Phi(r,t) = e^(-i omega t) int dV' rho_0(r) e^(i omega |r-r'|/c)/|r-r'|
> and
> A(r,t) = e^(-i omega t) 1/c int dV' j_0(r) e^(i omega |r-r'|/c)/|r-r'|.
>
> So we see that the potentials have the *same* time dependence as the
> charge and current density, i.e. both are periodic functions of the time
> with the *same* frequency as the densities. Since we are only interested
> in the time dependence, I will now introduce abbreviations for the
> integral and write simply
> Phi(r,t) = e^(-i omega t) Phi_0(r)
> and
> A(r,t) = e^(-i omega t) A_0(r).
>
> Now insert this into the equations (2) and (4); this gives:
> E = e^(-i omega t) (-grad Phi_0(r) + i omega/c A_0(r))
> and
> B = e^(-i omega t) rot A_0(r).
>
> So we see that the fields have the *same* *periodic* time dependence as
> the densities. In other words: if one has a charge and/or current
> density which changes periodically with a frequency f, there will be
> electric and magnetic fields which *also* change periodically with the
> *same* frequency f. This result is *completely* general, it does not
> depend on the frequency f in any way.
>
> The motion of the earth around the sun produces a charge and current
> density which changes periodically with a frequency of 1/1 year. Thus
> there will be electric and magnetic fields with that same frequency. In
> other words, there is an electromagnetic wave with a frequency of 1/1 year.
>
> If you want to know more details about that wave, you have to do
> the integrals (i.e. calculate A_0 and Phi_0), and then do the
> derivatives to get E and B. From that, you can get the Poynting vector
> S = c/4 pi (E cross B),
> which tells you how much energy is radiated in which directions.
>
> But all these details are rather irrelevant, since the basic thing was
> already proven above...
>
>
>
> > 1 fertz is a very acurate number
>
> That's a rather meaningless statement. 1 Hz, for example, is *also* a very
> accurate number.
>
>
>
> > (a mistake of your calculation of the order of 20 timwes
> > will be also accepted as a good result!!!....)
>
> Well, my proof shows that the motion of the earth around the sun
> produces electric and magnetic fields which have the *same* periodicity
> as the motion of the earth around the sun, i.e. a frequency of *exactly*
> 1/1 year. There is no error at all here - the frequency comes out *exactly*.
>
> -----------------------
that was very impressive
but still i didnt see the botom line in figures
you know i think that is i will insert numbers and
actual data i will get 1 Hertz not 1 fertz
what do you think about it?
am i wrong ???
letas see your figures!!(numbers)

btw dont you realise that you are making a bigger and bigger *** of
youself ?? do you think that the wole world is stoopid?
to fail to see that you are a crook? and a sore looser?
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