# Something wrong with Ampere's Law?

Discussion in 'Physics & Math' started by eram, Oct 1, 2015.

1. ### danshawenValued Senior Member

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Thanks for the warning. I will resist the urge, but I'm an electrical engineer also. More Faraday than Maxwell, I freely admit.

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3. ### Q-reeusBannedValued Senior Member

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Something I tried to pin down early on, but yes that is the general assumption. You and I were discussing definitions as a fork off the main topic.

5. ### danshawenValued Senior Member

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Very well. EXACTLY how is it that you expect that you will measure 'CURL?'

Even if you could measure it, do you imagine somehow that this could be done without affecting either the magnetic field at that point, or the current density of the wire?

Of course, if you already have a magnitude and direction for the curl, then you already have an expression for the current density too, right?

Why can't a stationary point charge appear to be moving relative to an observer riding an electron in the wire?

Last edited: Oct 2, 2015

7. ### Q-reeusBannedValued Senior Member

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Measuring, as opposed to the point definition, requires evaluation over a finite area, and then it's best to refer to the integral form of e.g. Maxwell-Ampere law.
Sure there is afaik no practical way to directly measure curl B in a current carrying wire, but neither is there a need. If you are doubting validity of M-A law, you could do the following:
Using identical X-section filamentary wires each carrying the same current, layer them in concentric sheaths - measuring the surface B at each stage of radial buildup. One should get a good approximation to |B|/r = constant. Confirming the validity of curl B. Of course you do have to assume that contribution to B interior to a cylindrical current sheath is zero - as demanded by use of Biot-Savart expression.
One example where it's easy to directly measure curl E, and via ME's, to then indirectly measure curl B, of a free-space plane EM wave, is via a receiving loop antenna. So what if measuring then perturbs - any back-reaction to source can be and usually is totally negligible.
Usually it works the other way round.
No reason I can think of. This is post 1905 after all.

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8. ### James RJust this guy, you know?Staff Member

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danshawen,

I see you went for the "more irrelevancies" option.

I think I'll wait for eram to re-appear in this thread, if he ever does.

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9. ### danshawenValued Senior Member

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What is irrelevant about pointing out that relativity allows a single point charge to possess a 'charge density' when in proximity of a current carrying wire? I'm certain, Maxwell himself would probably have taken issue with this interpretation of his vector equations. Nevertheless, it is consistent.

10. ### eramSciengineerValued Senior Member

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I think I'll have to work it out myself. Haha

These guys are terrible. Arguing over semantics and I haven't seen any maths regarding Biot-Savart law at all. Threads always get derailed.

11. ### Q-reeusBannedValued Senior Member

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NOTE: below post is the only one this thread needing a restoration following crash.

Q-reeus, Nov 4, 8:47PM
You began in #1 with an incorrect assertion:
It was then pointed out to you why this was wrong. Yes sidetracking unfortunately developed, but why show such disrespect by ignoring all respondents for more than a full month? And I noted you made the same opening post at another forum and around the same time (using another alias). Evidently feedback there also not up to scratch iyo.

What was (maybe still is) the reasoning for making the above claim? I did try to anticipate it in #2, maybe not clearly enough for the penny to drop. Wikipedia say or any decent textbook on EM covers the definition of vector identities including curl, in Cartesian, cylindrical, and spherical coordinates. With such a recipe, just apply it to your (assumed infinitely long, straight, steady curent) thin wire case, using the appropriate particularly simple Biot-Savart expression. Proving for yourself in vacuo curl B = 0.

12. ### 1100fBannedRegistered Senior Member

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First of all, we speak here of time independent fields and current density, so that the dE/dt part of Maxwell's equation is not relevant since it is equal to zero..
Now for the equation itself x B = μ0 J. This equation is in fact x B(x,y,z) = μ0 J(x,yz). So if we look at all the positions in space where J(x,y,z) = 0, at those same position you will have x B(x,y,z) = 0.
Notice that this does not mean that B(x,y,z) = 0.
For example, suppose that J(x,y,z) = 0 almost everywhere except inside an infinte cylinder of radius r and with axis being the z axis. J(x,y,z)= 0 for all x,y and z, except for sqrt(x^2 + y^2) < r ,where we have for example a constant current density J0 and in this case the total current is I = pi*r^2*J0 (This is is a current of a wire of radius r)
When you use Bio-Savart law, you know how to find the magnetic field. It will be given by the following description: the field does not depend on z, at equal distance from the wire the value of the magnetic field is the same and its direction at some point is orthogonal to the direction from the axis of the wire to that same point. Its magnitude will be given by: B(r) = μ0 I/r.
In a vector form you can write B(x,y,z) = μ0 I/(x^2 +y^2) x (y*i - x*j).
You can take the curl of this vector and verify that is equal to zero.
In fact what you have is a differential equation with boundary conditions.
If the equation would have been x B(x,y,z) = 0 for all x, y and z (with no exception) then the magnetic field would have been 0 every where. But this is OK, since J = 0 everywhere