- #36
kmarinas86
- 979
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DaleSpam said:EDIT: Btw, perhaps I should ask. Do you understand that the integral and the differential forms of Gauss' law are equivalent?
I -accept- that they are.
DaleSpam said:EDIT: Btw, perhaps I should ask. Do you understand that the integral and the differential forms of Gauss' law are equivalent?
I only mention 1 ft because I know that light travels at 1 ft/ns. The speed of light isn't such a nice number in cm.kmarinas86 said:You did not stick the context of the OP, and it has nothing to do with 1 ft.
Then I don't understand your whole question. If it is EM then by definition it satisfies Gauss' law, and it doesn't matter if you express it in the differential or in the integral form.kmarinas86 said:I -accept- that they are.
kmarinas86 said:If move the charge out of that sphere and then stop it 1 centimeter outside of it
pervect said:I think part of the machinery that makes field lines work is that you can write a general two-form as the sum of two wedge products of one-forms in 4 dimensions, and this is peculiair to 4-d. These two wedge products of one forms have a geometric interpretation as electric field lines and magnetic field lines, and their sum gives you the general rank two tensor. Unfortunately I'm going from memory here - I think this was mentioned briefly in MTW, but it's a huge book to search to find the section to refresh my memory about.
DaleSpam said:Do you really think it makes a difference?
DaleSpam said:If so, what is so special about cm and years that EM somehow does things in units of cm and years?
DaleSpam said:I.e. why do you think that the field will take exactly 1 year to update from a distance of 1 cm?
DaleSpam said:If you don't think that it makes a difference then why object?
kmarinas86 said:I didn't say it would change forever. I said, "Then, by definition the field near the charge, if made stationary after displacement, continues for 1 year to change..." This, means that for 1 year it continues to change.
And the last part, "...to reflect that the charge had been moved outside the sphere 1 year before." is about what happens 1 year later.
Khashishi said:How fast were you planning on moving that charge out of the sphere?
pervect said:It's not clear what sort of proposal you're thinking about, but if it's along some von-Flanderen ideas, it's well known that delay in the force will yield a non-conservation of angular momentum.
codelieb said:Feynman addresses this (so-called) paradox in the final paragraph of FLP Vol. II Chapter 27, Field Energy and Field Momentum:
"Finally, another example is the situation with the magnet and the charge,
shown in Fig. 27-6. We were unhappy to find that energy was flowing around
in circles, but now, since we know that energy flow and momentum are proportional,
we know also that there is momentum circulating in the space. But
a circulating momentum means that there is angular momentum. So there is
angular momentum in the field. Do you remember the paradox we described in
Section 17-4 about a solenoid and some charges mounted on a disc? It seemed
that when the current turned off, the whole disc should start to turn. The puzzle
was: Where did the angular momentum come from? The answer is that if you
have a magnetic field and some charges, there will be some angular momentum
in the field. It must have been put there when the field was built up. When
the field is turned off, the angular momentum is given back. So the disc in the
paradox would start rotating. This mystic circulating flow of energy, which at
first seemed so ridiculous, is absolutely necessary. There is really a momentum
flow. It is needed to maintain the conservation of angular momentum in the
whole world."
This, however, is merely a qualitative description; sufficient quantitative (mathematical) information about the energy and momentum of the electromagnetic field is given in this chapter that a Caltech sophomore in his second year of the Feynman Lectures course would be expected to be able to find the final angular frequency of the disc as a function of the various parameters it depends on.
Mike Gottlieb
Editor, The Feynman Lectures on Physics, Definitive Edition
---
Physics Department
California Institute of Technology
pervect said:I think part of the machinery that makes field lines work is that you can write a general two-form as the sum of two wedge products of one-forms in 4 dimensions, and this is peculiair to 4-d.
Similarly with 1 cm and 1 year, so I don't get why you object to replacing the 1 cm with 1 ft. That is all I was doing, because 1 ft is a more convenient small distance than 1 cm.kmarinas86 said:1 foot and 1 year taken together bears no relationship to the speed of light. Instead, it has a physically irrelevant speed of 9.65873546*10^-9 m/s, which has absolutely nothing to do with what is being discussed here.
Sorry about my confusion. I don't know how I could have possibly been so obviously mistaken as to think that "near" referred to the field 1 cm or 1 ft away from the charge when it so obviously should refer to the field 1 ly awaykmarinas86 said:I said, "Then, by definition the field near the charge, if made stationary after displacement, continues for 1 year to change..." ... In other words, the field (on the sphere) continues to change for 1 year
Ben Niehoff said:This has nothing to do with it. Field lines work because the source-free Maxwell equations imply that the 2-form F is harmonic.
Harmonic forms (in any dimension) have the distinction that they capture purely topological information. ...
Ben Niehoff said:This has nothing to do with it. Field lines work because the source-free Maxwell equations imply that the 2-form F is harmonic.
Harmonic forms (in any dimension) have the distinction that they capture purely topological information. If you integrate a harmonic n-form over a closed n-surface, the result is either zero or non-zero, depending on whether the n-surface encloses some topological feature (for example, a 1-surface on a cylinder might wrap around the cylinder...or a 2-surface in R^3 might enclose a charge). Any n-surface that encloses the same set of topological features must give you the same result.
You can think of this as a higher-dimensional analogue of contour integration. In fact, all analytic functions on the complex plane satisfy Laplace's equation, which is why contour integration works.
Matterwave said:I guess my question, what does F being harmonic have to do with field lines? It seems to me that Stokes theorem is sufficient in both (empty space and continuous charge) cases to justify the use of field lines.
The Lienard Wiechert potential is the convincing reason. The LW potential depends only on the motion of the charge at the retarded time. So the field at the near side updates with ~1 ns delay and the field at the far side updates with ~1 year delay. The field does not change outside of the times as indicated above.ARAVIND113122 said:i completely agree with kmarinas86. the field SHOULD continue to change for 1 year[approx].so far,none of the members have posted a convincing reason why it shouldn't.after all,information does take time to travel,and nothing happens instantaneously.once the charge is taken out of the sphere,the 'data' from the other side of the sphere would take time[almost 1 year] to reach the side that was initially closer to the charge