🚀 go-pugleaf

"Franz Heymann" <notfranz.heymann@btopenworld.com> wrote in message news:<c1ik59$k89$12@titan.btinternet.com>...
> "Sergey Karavashkin" <selftrans@yandex.ru> wrote in message
> news:a42650fc.0402241512.7788126e@posting.google.com...
> > "Dirk Van de moortel" <dirkvandemoortel@hotmail.Thanks-NoSperm.com> wrote
>  in message news:<c12pae$cd7$1@reader11.wxs.nl>...
> > > "Sergey Karavashkin" <selftrans@yandex.ru> wrote in message
>  news:a42650fc.0402161443.85012fb@posting.google.com...
> > > > "Dirk Van de moortel" <dirkvandemoortel@ThankS-NO-SperM.hotmail.com>
>  wrote in message
>  news:<NHIVb.13987$pC3.12117@news.cpqcorp.net>...
> > > > > "Sergey Karavashkin" <selftrans@yandex.ru> wrote in message
>  news:a42650fc.0402081450.153f158a@posting.google.com...
> > > > > > thoovler@excite.com (Igor) wrote in message
>  news:<d434b6c6.0402020056.7de6d18b@posting.google.com>...
> > > > > > > selftrans@yandex.ru (Sergey Karavashkin) wrote in message
>  news:<a42650fc.0402011435.6e84feaa@posting.google.com>...
> > > > > > > > Dear Colleagues,
> > > > > > > >
> > > > > > > > We open the new volume
> > > > > >
> > > > > > [snip]

> >
> > You can additionally make sure that curl(grad(phi)) =/= 0 looking at
> > our new dynamic animation of scalar potential produced by dynamic
> > dipole,
> 
> For *any* scalar function of position phi, it is universally true, as can be
> proved in two lines of vector calculus, that
> curl(grad(phi)) = 0
> 
> What am I missing?
> 
> Franz

Truly, Franz, you are one of not so many here whom I especially
respect for your knowledge and skill. Unfortunately, our relations
turned out so that we each time appeared on different sides of
barricade and you refused to penetrate into the core of issue. I
understand, if you go standard way in rigid frames of conventional 
formalism, the outcome curl(grad(phi)) = 0 is warranted. But the point
is not so as it seems in conventional formalism. To make sure, please
see the animation

http://selftrans.narod.ru/agV.gif

and determine by eye the integral over surface of selected volume,
supposing the area of cross-section normal to the screen. I suspect,
you will yield different values at different moments of time. That is
the entrance to Minotaur's labyrinth. ;-) At due time you seemingly
understood the feature of divergence theorem,

"On longitudinal electromagnetic waves. Chapter 1. Lifting the bans"
http://angelfire.lycos.com/la3/selftrans/archive/archive.html#long 

and "Transformation of divergence theorem in dynamical fields"
http://angelfire.lycos.com/la3/selftrans/archive/archive.html#div 

This is why I suggest to start from this reference point for further
understanding. After this we have to leave aside all habitual
standards and scrutinize the essence of computations as such, however
unusual they seem. Please read our

"Theorem of curl of a potential vector in dynamical fields"
http://angelfire.lycos.com/la3/selftrans/v2_2/contents.html#curl

You will see its value in dynamic fields irrespectively of potential
function of flux. After this read please our

"On gradient of potential function of dynamic field" 
http://selftrans.narod.ru/v4_1/grad/grad01

and determine, to what is it equal in dynamic fields. After this all,
connect the results - you will yield what I'm saying about. ;-)

It is also important, if you see the animation where I presented for
Dirk the diagram of scalar potential of dynamic dipole

http://selftrans.narod.ru/agfig4.gif

and look at the area of perpendicular to the axis of dipole, you will
see that gradient not always is along the field propagation. In this
area it is perpendicular to the propagation. It is important in view
that when perpendicularly oriented, the curl of this DYNAMIC vector is
not zero.

Of course, this is far from all, but you will make a great step to
understanding. If my problems with posting to Google are not growing
(by some reason, last time their machine rejects my posts, replying to
the very first, "too much letters for today"), I will gladly discuss
this subject further with you.

Kind regards,

Sergey