Experimental evidence against Gauss' law

In summary, the conversation discusses the results of an experiment involving a magnet, a coil, and an oscilloscope. The oscilloscope shows that the signal resembles the derivative of a Gaussian function, indicating a maximum of magnetic flux when the magnet is in the center of the coil. The discussion then delves into the relevance of Gauss' law and Faraday's law, with the conclusion that the experiment is better explained by Faraday's law. The conversation also suggests using a larger coil and an integrator to obtain more accurate results. Overall, the conversation highlights the importance of conducting experiments in a controlled and precise manner to verify established laws.
  • #1
htg
107
0
I have a 5mm diameter, 10mm long magnet, a short (6mm) coil of 50mm diameter, and an oscilloscope. When I move the magnet through the coil, the oscilloscope shows that the signal (voltage) looks pretty much like the derivative of a Gaussian function. So there must be magnetic flux maximum when the magnet is in the center of the coil.
According to the Gauss law, there should be a minimum of flux placed between two maxima (when the magnet is in the center of the coil, the flux that goes through the magnet comes back on the outside of the magnet and mostly inside the coil, because the coil is large).
What should I think about it?
 
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  • #2
htg said:
(when the magnet is in the center of the coil, the flux that goes through the magnet comes back on the outside of the magnet and mostly inside the coil, because the coil is large)

I think your coil is much too small to "contain" the field (almost) completely. Try it with a much larger diameter coil, e.g. 1 meter.
 
  • #3
htg said:
What should I think about it?
The first thing that you should think is that it is experimental evidence against the validity of your experiment. It might test Faraday's law, but it certainly doesn't seem to have anything to do with Gauss' law to me.
 
  • #4
jtbell said:
I think your coil is much too small to "contain" the field (almost) completely. Try it with a much larger diameter coil, e.g. 1 meter.
I partially went along your suggestion and I made a 200mm diameter coil.
At distances several times the size of the magnet the H field decreases like 1/r^3, so since the radius of my coil is 10 times greater than the length of the magnet, I can expect that H field is only about 0.001 of the H field near the magnet, and that 99.5% of the flux returning through the air goes through the inside of the coil. It is pretty clear that I do not need larger coil. The signal still looks the same.
 
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  • #5
It doesn't matter how large you make your loop. Your experiment is simply not relevant to Gauss' law for magnetism. The results you are describing are exactly what you would expect to see by Faraday's law.
 
  • #6
DaleSpam, obviously it is relevant: you can easily infer from the Gauss' law that the fux through the plane of symmetry of the magnet, which is perpendicular to magnet's axis is zero. For large enough coil it should be close to zero when the magnet is in the center of the coil. But when the magnet is shifted along its axis, there is significant flux through the coil if the magnet is reasonably close to the plane of the short coil.
 
  • #7
Try these variations on your experiment:
1) move the magnet to the point of highest signal and stop. What is the voltage?
2) move the magnet through at different speeds. How does that affect the voltage?
3) move the magnet backwards through the coil. What is the polarity of the voltage compared to forwards?

Then ask yourself. Based on this, is your device sensitive to flux, or to changes in flux?
 
  • #8
Of course to changes in flux.
If you know the derivative of a function and you know that the function rapidly decreases to zero as x increases, you can tell what the function is.
 
  • #9
htg said:
Of course to changes in flux.
Therefore the operating principle of your device is Faraday's law, not Gauss' law. It behaves exactly as you would expect it to according to Faraday's law.
 
  • #10
The signal you are getting from your coil is a transient signal, and does not provide a suitable signal for quantitative analysis. The common coil geometry for these measurements is called a Rogowski coil, and the associated electronics is based on Faraday's Law:

Although the Faraday Law as normally written applies only to ac fields, it can be written in the following way:

V = -(d/dt)N∫B·dA volts (Faraday Law)

so by carrying the dt to the other side and integrating we get

∫V·dt =V·(t2 - t1) = -N∫B·dA = - N·A·(B2 - B1) (volt-seconds)

So you need to build a simple voltage integrator. These can be built with a single low leakage op-amp. See my posts in the following thread:

https://www.physicsforums.com/showthread.php?t=391463&highlight=integrating+coil

Bob S
 
  • #11
Coceivably I could build an integrator, but clearly I can perform qualitative analysis of the experiment without it - it is easy to imagine what the antiderivative will look like. And it will be a function whose graph is bell-shaped with maximum corresponding to the position of the magnet in the center of the coil.
 
  • #12
htg said:
Coceivably I could build an integrator, but clearly I can perform qualitative analysis of the experiment without it - it is easy to imagine what the antiderivative will look like. And it will be a function whose graph is bell-shaped with maximum corresponding to the position of the magnet in the center of the coil.
Which is correct. It is what your experiment is giving and it is what is expected from Maxwell's equations.
 
  • #13
You are seeing exactly what I would expect you to see.

You are passing a small magnet through a short coil, presumably along the axis, from some distance on one side to the same distance on the other side.

Because it is short, the B field around the magnet will look like a very fat toroid.

The current created by the motion will depend on the rate at which the field changes with distance from the magnet - that rate is higher close to the magnet so most likely you will see a single, roughly gaussian pulse of current. But depending on precisely how you move the magnet, you could get all sorts of results.

If you want to verify (or disprove) established laws, it's sensible to perform the classic experiments, which are designed to produce a 'clean' situation to test a single clear hypothesis without introducing unnecessary extraneous factors.
Contrary to popular belief, adding confusion does not improve a case.
 
  • #14
As I explained in post#1 and #4, when the magnet is in the center of the large coil, the flux through the coil should be near 0 according to Gauss' law, because the flux through the magnet is almost canceled by the flux returning through air, mostly inside the coil.
 
  • #15
You seem to be confused about the difference between electric and magnetic fields.

Gauss's law, also known as Gauss's flux theorem, is a law relating the distribution of electric charge to the resulting electric field. Gauss's law states that:
The electric flux through any closed surface is proportional to the enclosed electric charge.
 
  • #16
I think I see your problem. You have not actually done the math so you think that these two statements are contradictory:
htg said:
For large enough coil it should be close to zero when the magnet is in the center of the coil.
htg said:
it will be a function whose graph is bell-shaped with maximum corresponding to the position of the magnet in the center of the coil.

In fact, they are both correct and not contradictory. For a magnetic dipole moment m placed at a distance z along the axis of a loop of radius R the magnetic flux through the loop is:

[tex]\frac{m R^2 \mu _0}{4 \pi \left(R^2+z^2\right)^{3/2}}[/tex]

This function is a nice bell-shaped function with a maximum at z=0 for any finite R. The derivative wrt z is two peaks of opposite polarity which, by Faraday's law, is the voltage waveform you should get if you move it through at constant speed and experimentally what you are getting. As R goes to infinity the function goes to zero everywhere, including at the maximum which is always at z=0.
 
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  • #17
AJ Bentley said:
You seem to be confused about the difference between electric and magnetic fields.

Gauss's law, also known as Gauss's flux theorem, is a law relating the distribution of electric charge to the resulting electric field. Gauss's law states that:
The electric flux through any closed surface is proportional to the enclosed electric charge.
There's an analogous Gauss's law for magnetic fields. (See: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/maxeq2.html#c2")
 
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  • #18
Suppose your magnet moved towards,through and then emerged from the coil at steady speed.As the magnet approaches the coil the induced emf rises to a maximum at the closest distance of approach,it drops as the magnet moves into the coil where it reaches a zero value and then it reverses reaching a maximum as the magnet just leaves.Thereafter,as the distance of retreat increases the emf drops.If the speed is constant the graph of emf against time or distance would be symmetrical about the centre of the system the emfs on emergence being in the opposite directions to those on appproach.If the speed is not constant there would not be the above symmetricality but there would still be a reversal of emf direction about the centre of the system.I suggest you have another look but make the magnet pass all the way into and out of the coil.
 
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  • #19
DaleSpam said:
I think I see your problem.
For a magnetic dipole moment m placed at a distance z along the axis of a loop of radius R the magnetic flux through the loop is:

[tex]\frac{m R^2 \mu _0}{4 \pi \left(R^2+z^2\right)^{3/2}}[/tex]

This function is a nice bell-shaped function with a maximum at z=0 for any finite R. The derivative wrt z is two peaks of opposite polarity which, by Faraday's law, is the voltage waveform you should get if you move it through at constant speed and experimentally what you are getting. As R goes to infinity the function goes to zero everywhere, including at the maximum which is always at z=0.
You have discovered where the problem was. Thank you.
 
  • #20
You are welcome.
 

1. What is Gauss' law and how does it relate to experimental evidence?

Gauss' law is a fundamental law in electromagnetism that states that the electric flux through a closed surface is equal to the charge enclosed by that surface. Experimental evidence against Gauss' law refers to any observed discrepancies or violations of this law in real-world experiments, which can help refine and improve our understanding of the underlying principles.

2. What are some examples of experimental evidence against Gauss' law?

One example is the discovery of magnetic monopoles, which are particles with only a single magnetic charge. This challenges Gauss' law, which states that all magnetic fields must have both a north and south pole. Other examples include the observation of non-conservative electric fields, which do not follow the usual rules of Gauss' law.

3. How do scientists reconcile these experimental findings with Gauss' law?

Scientists use advanced mathematical models and theories to explain and incorporate the observed discrepancies into our understanding of electromagnetism. For example, the existence of magnetic monopoles can be explained by using the Dirac monopole theory, which introduces a new term to Gauss' law to account for the single magnetic charge.

4. Can Gauss' law still be considered a valid law in light of these experimental findings?

Yes, Gauss' law is still considered a valid law in electromagnetism. It is a highly accurate and useful tool for understanding electric and magnetic fields in most situations. However, experimental evidence against it highlights the need for further research and refinement of our understanding of electromagnetism.

5. How does experimental evidence against Gauss' law impact current and future research?

Experimental evidence against Gauss' law can lead to the development of new theories and models that better explain and predict real-world phenomena. It also highlights the importance of continued experimentation and observation in the scientific method, as well as the need to constantly revise and improve our understanding of fundamental laws.

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