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Science Forum Index » Physics Forum » One question about Maxwell's equations
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| alb |
 Posted: Sat Apr 26, 2008 2:16 am |
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I would like to ask if you think that integral and differential forms
of Maxwell's equations are really equivalent or if there are some
phenomena that one form can describe and the other not. Thanks in
advance. |
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| Benj |
| Posted: Sat Apr 26, 2008 6:21 am |
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alb wrote:
Quote: I would like to ask if you think that integral and differential forms
of Maxwell's equations are really equivalent or if there are some
phenomena that one form can describe and the other not. Thanks in
advance.
Close but no cigar. The problem is not in the differences between the
differential and integral forms, but rather in that these equations
are not written in CAUSAL form. Thus, the phenomena which is NOT
described by them is "causality". This leads to all manner of sloppy
thinking such as the belief that E and H fields "create each other".
But Maxwells equations are inherently causal and can be written in
causal form. [The difference is that the usual equation simply says
that one side of the equation is EQUAL TO the other side. The causal
form says that one side is CAUSED BY the other side as a source.] See
the books by Jefimenko for more details.
Benj |
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| Benj |
| Posted: Sat Apr 26, 2008 6:45 am |
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On Apr 26, 11:38 am, "Androcles" <Headmas...@Hogwarts.physics> wrote:
Oh you mean "cretins" like James Clerk Maxwell himself? Maxwell could
never figure out how "curl" worked and hence proposed a "ball bearing"
theory to deal with the problem of elements rotating against
themselves?
And that wiki article really shows the problems with Maxwell and
Faraday. One needs to ask just how in hell does "flux" through a
contour create a so-called "E" field? This happens even in regions of
zero B (outside a long solenoid or toroid). Therefore this theory is
a remnant of the long-discredited "action at a distance" theories.
Even though it is eminently practical for the design of motors,
transformers, and the like, it is clearly a bogus theory. What is
obviously going on is that there is SOME OTHER MECHANISM of induction
while the "flux" rule is simply a calculation which just happens to
(usually, but not always) ALSO give the correct answer. But the flux
rules are NOT the correct mechanism for the phenomena. Yeah, it's
about time for people to go back and give Maxwell and Faraday a second
hard look.
Benj
Hint: Experiments such as the Aharonov-Bohm effect strongly suggest
that the true induction phenomena is related to the magnetic vector
potential "A" rather than to the magnetic field "B" or a "flux" of
it.
OF course chances of Andro working out a correct answer here are nil. |
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| Igor |
| Posted: Sat Apr 26, 2008 7:28 am |
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On Apr 26, 8:16 am, alb <ufgk...@yahoo.it> wrote:
Quote: I would like to ask if you think that integral and differential forms
of Maxwell's equations are really equivalent or if there are some
phenomena that one form can describe and the other not. Thanks in
advance.
Unless there are flaws in the theorems of vector calculus, they have
no choice but to be equivalent. |
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| Androcles |
| Posted: Sat Apr 26, 2008 10:38 am |
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| Timo A. Nieminen |
| Posted: Sat Apr 26, 2008 3:28 pm |
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On Sat, 26 Apr 2008, alb wrote:
Quote: I would like to ask if you think that integral and differential forms
of Maxwell's equations are really equivalent or if there are some
phenomena that one form can describe and the other not. Thanks in
advance.
They're equivalent in that you can convert one form to the other. But they
different in practice.
(a) The differential form can't be used at points where the fields are
discontinuous. For example, at an interface between two different media,
the differential form doesn't work. You can use the differential equations
in each of the media individually, but you need some boundary conditions
relating the fields on each side of the interface. Most good EM textbooks
will give a derivation of the boundary conditions, from the integral
equations.
(b) The integral equations won't (easily) tell you the field at a
particular point. If this is what you're trying to find out, try the
differential equations instead. Where fields are known, and you're trying
to find the total charge enclosed by the surface, the integral form is
excellent. Also, when symmetry makes it easy to integrate, as in the usual
applications of Gauss's law.
--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html |
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| Dirk Van de moortel |
| Posted: Sat Apr 26, 2008 4:16 pm |
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| Benj |
| Posted: Sun Apr 27, 2008 5:04 am |
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On Apr 26, 4:28 pm, "Timo A. Nieminen" <t...@physics.uq.edu.au> wrote:
Quote: On Sat, 26 Apr 2008, alb wrote:
I would like to ask if you think that integral and differential forms
of Maxwell's equations are really equivalent or if there are some
phenomena that one form can describe and the other not. Thanks in
advance.
Hey, TOTALLY GREAT post Timo!
( I calls 'em like I sees 'em!)
-----------------------------------
Quote: They're equivalent in that you can convert one form to the other. But they
different in practice.
(a) The differential form can't be used at points where the fields are
discontinuous. For example, at an interface between two different media,
the differential form doesn't work. You can use the differential equations
in each of the media individually, but you need some boundary conditions
relating the fields on each side of the interface. Most good EM textbooks
will give a derivation of the boundary conditions, from the integral
equations.
(b) The integral equations won't (easily) tell you the field at a
particular point. If this is what you're trying to find out, try the
differential equations instead. Where fields are known, and you're trying
to find the total charge enclosed by the surface, the integral form is
excellent. Also, when symmetry makes it easy to integrate, as in the usual
applications of Gauss's law.
--
Timo Nieminen - Home page:http://www.physics.uq.edu.au/people/nieminen/
E-prints:http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits:http://www.users.bigpond.com/timo_nieminen/spirits.html |
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