# Experimental evidence against Gauss' law

1. Aug 17, 2010

### htg

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?

2. Aug 17, 2010

### Staff: Mentor

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. Aug 17, 2010

### Staff: Mentor

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. Aug 17, 2010

### htg

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.

Last edited: Aug 17, 2010
5. Aug 17, 2010

### Staff: Mentor

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. Aug 17, 2010

### htg

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. Aug 17, 2010

### Staff: Mentor

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. Aug 17, 2010

### htg

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. Aug 17, 2010

### Staff: Mentor

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. Aug 17, 2010

### Bob S

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:

Bob S

11. Aug 17, 2010

### htg

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. Aug 17, 2010

### Staff: Mentor

Which is correct. It is what your experiment is giving and it is what is expected from Maxwell's equations.

13. Aug 17, 2010

### AJ Bentley

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. Aug 17, 2010

### htg

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 cancelled by the flux returning through air, mostly inside the coil.

15. Aug 17, 2010

### AJ Bentley

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. Aug 17, 2010

### Staff: Mentor

I think I see your problem. You have not actually done the math so you think that these two statements are contradictory:
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:

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

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.

Last edited: Aug 17, 2010
17. Aug 17, 2010

### Staff: Mentor

There's an analogous Gauss's law for magnetic fields. (See: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/maxeq2.html#c2")

Last edited by a moderator: Apr 25, 2017
18. Aug 17, 2010

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.

Last edited: Aug 17, 2010
19. Aug 17, 2010

### htg

You have discovered where the problem was. Thank you.

20. Aug 17, 2010

### Staff: Mentor

You are welcome.