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Why I doubt the generality of Gauss' law: A Gaussian sphere 1 light year across 
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#19
Feb1912, 03:01 PM

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#20
Feb1912, 03:02 PM

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EDIT: I guess I couldn't stop asking questions :D 


#21
Feb1912, 03:25 PM

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The integral form of Gauss' law follows mathematically from the differential form.
So if one form of the law doesn't seem blindingly intuitive, look at the other. (And I suppose it wouldn't hurt to study the proof of how you derive one from the other, as well.) If both don't seem blindingly intuitive, look at the experimental results supporting them... 


#22
Feb1912, 03:33 PM

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As has been pointed out before, the "field lines" picture will make this bleedingly obvious. Gauss' Law just counts field lines going through a surface. Field lines always end on the charge, no matter how the charge wiggles about. So it becomes a simple topological problem: If the charge is inside the sphere, any field lines going from the charge to infinity must cut through the sphere. Likewise, if the charge is outside, any field lines must either avoid the sphere or cut it twice; once in, once out.
Note: The entire field line picture is dependent on the 1/r^2 nature of the force. 1/r^2 forces in 3 dimensions are very special; they have the property that they can be described by a field line picture. (Mathematically, this has to do with harmonic differential forms.) 


#23
Feb1912, 03:34 PM

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A 10 meter device would require measurements at a rate of nearly 30 million times per second. For, a 1 meter device, it would need to be nearly 300 million times a second. I don't know any specifics, but I suppose it is a safe bet that at those the frequencies, the accuracy (lack thereof) wouldn't be counted on, so actual measurements would not be quick enough to pick up the "time delay" in the update of the electrical field. The "time delay" is the whole point of this argument I'm making. 


#24
Feb1912, 04:43 PM

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#25
Feb1912, 04:45 PM

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#26
Feb1912, 04:52 PM

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Does the field near the charge, if made stationary after displacement, continue for 1 year to change in a way compensating exactly the field far of it as it updates the far end of the sphere 1 light year away to reflect that the charge had been moved outside the sphere 1 year before? EDIT: I guess I couldn't stop asking questions :D 


#27
Feb1912, 08:25 PM

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Spoiler
1) For a point charge, yes, the integrated flux is discontinuous. For an extended charge distribution, no.
2) No, the field at a given event depends only on the charge, position, velocity, and acceleration of the charge at the retarded time. 


#28
Feb2312, 09:19 AM

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#29
Feb2312, 11:23 AM

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It does not continue to change for a year simply because you have drawn a Gaussian surface out 1 light year distant. After all, how would it know if you have drawn your surface out 1 year or 2 or 2 million? Furthermore, the fact that it has stopped changing at one part of the surface and continues to change at another part of the surface does not in any way contradict Gauss' law. 


#30
Feb2312, 12:27 PM

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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. If we go by the "field lines" argument to show how this is done for a negative charge moved out of the sphere, the number of lines into the sphere = the number of those going out, which is easy to imagine, we would have field lines that point away from the "line" overlapping the charge's displacement, poking through a surface immediate to the point through the sphere that the charge crossed. This would be like having an "effective" positive charge inside that part of a sphere and cancels out the "effective" negative charge at the other side of the sphere. If this is what happens, then I can see how one can arrive at Gauss's law. Theory says this is the case, but what about the fact that the Liénard–Wiechert potential is not always valid? Then these field lines may take on a different shape. But why must field lines behave this way? 


#31
Feb2312, 01:46 PM

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Hello,
You can try to picture the situation in a more familiar way. Think about a flat sheet with a stone leaning in some point. The weight of the stone will curve the sheet in such a way that measuring the displacement along a closed line surrounding the stone, with respect the "nostone" configuration, you can argue the exact value of the mass of the stone (gauss theorem). When you move the stone to another point a wave is emitted on the sheet surface "updating" the value of the displacement. The displacement in a given point remains costant except for the time the wave passes onto it; it does not continue to change for the whole duration of the wave (except if the stone continue moving, wich is not the case). At any given time, the displacement on a closed line will tell you whether or not that line surrounds the stone. The value of the displacemtent ON the wave will compensate for the fact that points not yet reaced by the wave have their "old" value. P.s. Sorry for my bad english ^^ P.p.s. I hope you didn't need a rigorous treatment. If you are interested in how it can be possible that the filed always satisfy the gauss theorem, the reason is substantially topological. Ilm 


#32
Feb2312, 03:47 PM

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EDIT: Btw, perhaps I should ask. Do you understand that the integral and the differential forms of Gauss' law are equivalent? 


#33
Feb2312, 04:21 PM

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It's not clear what sort of proposal you're thinking about, but if it's along some vonFlanderen ideas, it's well known that delay in the force will yield a nonconservation of angular momentum. Anyway, supporting alternate theory development isn't somethign that we really do here, so I'm not going to comment in detail. 


#34
Feb2312, 04:35 PM

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#35
Feb2312, 04:39 PM

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#36
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