Path: ccsf.homeunix.org!ccsf.homeunix.org!news1.wakwak.com!nf1.xephion.ne.jp!onion.ish.org!honnetnews!news.gw.fukushima-u.ac.jp!news.tains.tohoku.ac.jp!newsfeed.media.kyoto-u.ac.jp!priapus.visi.com!orange.octanews.net!news-out.visi.com!petbe.visi.com!news.octanews.net!dimensional.com!pulsar.dimensional.com!newsfeed.frii.net!newsfeed.frii.net!news.compaq.com!news.cpqcorp.net!53ab2750!not-for-mail From: "Dirk Van de moortel" Newsgroups: sci.physics,sci.physics.electromag,alt.sci.physics.new-theories,fj.sci.matter,sci.physics.relativity References: Subject: Re: Gradient of potential function of dynamic field Lines: 142 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2800.1158 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1165 Message-ID: Date: Wed, 25 Feb 2004 11:13:37 GMT NNTP-Posting-Host: 16.183.16.62 X-Complaints-To: abuse@HP.com X-Trace: news.cpqcorp.net 1077707617 16.183.16.62 (Wed, 25 Feb 2004 03:13:37 PST) NNTP-Posting-Date: Wed, 25 Feb 2004 03:13:37 PST Organization: Hewlett-Packard Company Xref: ccsf.homeunix.org fj.sci.matter:109 "Sergey Karavashkin" wrote in message news:a42650fc.0402241512.7788126e@posting.google.com... > "Dirk Van de moortel" wrote in message news:... > > "Sergey Karavashkin" wrote in message news:a42650fc.0402161443.85012fb@posting.google.com... > > > "Dirk Van de moortel" wrote in message > > news:... > > > > "Sergey Karavashkin" wrote in message news:a42650fc.0402081450.153f158a@posting.google.com... > > > > > thoovler@excite.com (Igor) wrote in message news:... > > > > > > selftrans@yandex.ru (Sergey Karavashkin) wrote in message news:... > > > > > > > Dear Colleagues, > > > > > > > > > > > > > > We open the new volume > > > > > > > > > > [snip] > > > > > > > > > > > > > > Please enjoy reading full text: > > > > > > > > > > > > > > http://angelfire.lycos.com/la3/selftrans/v4_1/contents4.html#grad > > > > > > > > > > > > > > I hope, it will be interesting for many of you, and look forward to > > > > > > > hear your opinion. > > > > > > > > > > > > > > Sergey. > > > > > > > > > > > > There seems to be a mistake on the first page, where you have a scalar > > > > > > function dependent on both the radial coordinate and angle theta. But > > > > > > when you take the gradient, you only have a radial component but no > > > > > > angular one. This is why you're concluding that curl grad is not > > > > > > zero, when, once you do it properly, it must be. Curl grad must > > > > > > always vanish regardless of the nature of the coordinate system. It's > > > > > > an elementary theorem of vector calculus. I hope this has been > > > > > > helpful. Good luck. > > > > > > > > > > > > > > > Dear Igor, > > > > > > > > > > I understand you. You show the most typical reaction to this cycle of > > > > > our papers: "Something is wrong! Where is the mistake?" Merely > > > > > psychologically, you already do not consider how much logic is the > > > > > proof, how much correct is mathematics, you only filter the material, > > > > > seeking the trick. > > > > > > > > Looking at your > > > > http://selftrans.narod.ru/v4_1/grad/grad02/grad02.html > > > > we immediately see that your equation (4) is wrong since > > > > phi depends on theta in your equation (3). > > > > In your case where alpha is constant and zero, you should > > > > write: > > > > grad(phi) = @phi/@r e_r + 1/r @phi/@theta e_theta > > > > Your equation (5) for the curl is okay. > > > > So your equation (6) is wrong. > > > > > > > > Compare with the correct expressions for grad in eq (3) > > > > and curl in eq (72) in spherical coordinates: > > > > http://164.8.13.169/Enciklopedija/math/math/s/s571.htm > > > > Note that: > > > > your phi is their F > > > > your alpha is their theta > > > > your theta is their phi > > > > > > > > You made a very elementary mistake. > > > > > > > > Dirk Vdm > > > > > > Thank you, Dirk. At last I see that someone analyses our work, not > > > trying to thoughtlessly squeeze it into the procrustean bed of dogmas. > > > Though this inaccuracy which you have found does not effect on the > > > conclusion that curl of gradient does not vanish, none the less, I'm > > > very pleased. I fully agree with you, gradient of scalar potential has > > > to contain not only radial but also tangential component. Our analysis > > > that you can find some further in this paper, in the problem of field > > > of oscillating potential source - formula (14) in the page 7 - > > > corroborates this. > > > > > > To show that the inaccuracy you found will not turn to zero the curl > > > of gradient, I have put the derivation to our web site, > > > > > > http://selftrans.narod.ru/v4_1/grad/dirk/dirk.html > > > > > > because, on one hand, I think this question interesting and > > > long-expected, and on the other hand, because the derivation consists > > > of many long computations which are convenient to be read in the > > > standard appearance. > > > > Sergey, you made a new mistake here. > > On that page > > http://selftrans.narod.ru/v4_1/grad/dirk/dirk.html > > you "corrected in red" my equation > > grad(phi) = @phi/@r e_r + 1/r @phi/@theta e_theta > > to > > grad(phi) = @phi/@r e_r + 1/r 1/sin(theta) @phi/@theta e_theta > > but that is wrong, since I explicitly referred to > > http://164.8.13.169/Enciklopedija/math/math/s/s571.htm > > where in their equations (30) and (72), as I added: > > | your phi is their F > > | your alpha is their theta > > | your theta is their phi !!! > > > > Since your theta is their phi, my equation > > grad(phi) = @phi/@r e_r + 1/r @phi/@theta e_theta > > was okay and you should not have introduced the 1/sin(theta). > > After all, this is how *you* derived *your* equation (5). > > > > So, do try again, check the equations, make the substitutions > > | your phi is their F > > | your alpha is their theta > > | your theta is their phi !!!and you'll see that > > and verify that indeed > > curl(grad(phi)) = 0 > > It is a very well known elementary theorem. > > > > Dirk Vdm > > No, Dirk. To understand, who of us is correct, determine the axis of > symmetry of the problem and the angle corresponding to this symmetry. > The term of expression that contains this angle will be with the > coefficient 1/r. Both in the Leo's problem (this is seen in his > figure) and in the literature to which I referred responding him, the > angle theta does not correspond to the angle to which the symmetry of > the system relates. So to this term of expression > relates the coefficient 1/sin(theta). Dirk, this is not my wish. This > is the school program. So please see attentively this course to make > sure in what I'm saying. > > You can additionally make sure that curl(grad(phi)) =/= 0 looking at > our new dynamic animation of scalar potential produced by dynamic > dipole, > > http://selftrans.narod.ru/agfig4.gif > > In dynamic fields everything is not so as you used to think. So please > try to grasp what I'm saying before thinking me wrong. > > Kind regards, > Sergey You have swapped the two angular coordinates between applying grad and curl. Check it. Dirk Vdm