Re: MAXWELL's EQUATIONS OF THE ELECTROMAGNETIC FIELD!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

[G. Morgan <alarmpro@xxxxxxxxxxx>]

I've been wondering about that all day.   Thanks for the good
information!






On Sun, 10 Sep 2006 01:31:17 GMT, "NILS BÖRJESSON"
<borje@xxxxxxxxxxxx> wrote:

>By : Ove Tedenstig
>     Idungatan 37, 19 551 M{rsta
>     Sweden
>
>MAXWELL's EQUATIONS OF THE ELECTROMAGNETIC FIELD
>
>
>The nucleus of James Clerk Maxwell's electromagnetic theory from
>
>
>
>
>
>1867 consist of a set of formulae which describe the behavior of
>
>
>electric and magnetic field proparation. The theory was from
>the beginning an "aether" or mechanical theory, but this
>interpretation of electromagnetism later on was denyed.
>Today only a barren shell of mathemaical formalism reaminds
>which not say much of cause and source of electromagnetism.
>The scientific value of these formulae therefore may be put into
>question since they seem to have be overestimated in importance.
>
>However, the most famous are:
>
>(44a) ==========================
>
>        __ _
>        !/ E = 0               The electric field at free
>                               radiation from ap point source
>(44b) ==========================
>        __ _
>        !/ B = 0               The magnetic field at free
>
>
>(44c) ==========================
>
>       __ _      _
>       !/ E = -D B/Dt          ( D is the partial derivative)
>
>(44d) ==========================
>
>       __ _       2    _
>       !/ B = (1/c ).D E/ Dt
>
>
>
>DERIVING THE FORMULAE
>
>Because of limit of space, 44a and 44b are not derived here.
>However, it is a relatively easy task to get these results,
>which are achived by deriving the field strength out from an
>electric or magnetic point source in respect to its coordinates,
>x,y and z. Therefore, we concentrate ourselves only on the two
>remaining formulae, which mainly are got by vectorially
>manipulating the base equation (30). (44c) is achived by taking
>the time derivative of this equation, the (44d) is got by
>taking the space derivative of it.
>
>
>(45) ================================
>          _   _
>     _    E x v
>     B = ----2--        (from 30)
>            c
>                     _   _
>      _              E x v
>     DB/Dt = D/Dt ( ----2---- ) =
>                       c
>
>
>     __ _   2 _   _       2  2   __   _
>     !/ v/ c.(E x v ) = -v /c .( !/ x E )
>
>                         __   _
>     For v=c   DB/Dt = - !/ X E
>
>(46) ===================================================
>
>     __   _     __     _   _  2
>     !/ x B  =  !/ x ( E x v/c )
>
>
>__   _    _         __ _      _  __  _   _  __ _
>!/ x B = DE/Dt - v( !/.E ) - (E. !/).v + E( !/.v )
>
>!------------/   !-----------------------------------/
> Result           Will be zero for a non accelerating
> according to     point source
> Maxwell
>
>
>    __   _    _
>    !/ x B = DE/Dt        The result in accord with
>                          Maxwell valid for a non
>                          accelerating point source
>
>==========================================================
>
>
>LIGHT AND ELECTROMAGNETIC WAVES
>
>Beside these famous equations treated above, historically Macwell
>is famous for predicting electromagnetic fields propagating in
>in the same way as light in free space. The conclusions were made
>on basis of comparing results from the general wave equation based
>on how sound in air or mechanical waves were propagating in a medium,
>air and water for instance. But the modern physics do not confess
>any existence of a light bearing aether, and the contradictionary
>problem in Maxwell's theories therefore still remain.
>
>Vectorial manipulations are performed on results from (45) and (47)
>as shown in below.
>
>(48) ================================================
>
>  __   _     _
>  !/ x E = -DB/Dt              (from 45)
>
>  __   _      2        _
>  !/ x B = 1/c . D/Dt .E       (from 47)
>
>
>  __      __   _        __2 _    __  __ _        __2 _
>  !/ x (  !/ x E ) ? -  !/  E +  !/( !/ E ) = -  !/  E
>    __ _
>  ( !/ E is equal to zero for a point source )
>
>
>   __      __   _       __  _               __   _
>   !/ x (  !/ x E ) = - !/(DB/Dt) = - D/Dt( !/ x B ) =
>
>           2     _        2  2   2 _
>   D/Dt(1/c.D/Dt.E ) = 1/c .D /Dt .E
>
>     __ _      2   2   2 _
>   - !/ E = 1/c . D /Dt .E
>
>
>
>
>(49) =====================================================
>
>  __   _    _
>  !/ x E = DB/Dt              (from 45)
>
>  __   _      2      _
>  !/ x B = 1/c .D/Dt.E        (from 47)
>
>  __   __   _        __2 _     __  __ _       __2 _
>  !/x( !/ x B ) =  - !/  B  +  !/( !/ B ) = - !/  B
>
>     __ _
>  (  !/ B is zero for a point source =
>
>
>  __      __   _      __     2      _
>  !/ x (  !/ x B ) =  !/( 1/c. D/Dt.E ) =
>
>     2        __   _        2   2   2 _
>  1/c .D/Dt(  !/ x E ) = 1/c . D /Dt .B
>
>    __2 _      2   2   2 _
>  - !/  B = 1/c . D /Dt .B
>
>=======================================================
>
>
>The general wave equation is written :
>
>
>(50) =============================
>
>   __2        2   2   2
>   !/  Y = 1/v . D /Dt  . Y
>
>==================================
>
>The mathematical structure of (48),(49) and (50) is the same
>and it was this mathematical equivalency which gave Maxwell
>the idea of light being a medium carried wave. Since then many
>experiments have been perfomed by light, clearly showing that
>no active light aether do exist. Only the mathematical
>equivalency reamin intact.
>
>
--

-Graham
(remove the double e's to email)