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SIMPLE VISUAL DEMONSTRATION OF THE FARADAY’S DISC PARADOX (AND CORRESDPONDING SYMMETRY BREAKING PHENOMENA)

Created: Tuesday, 08 April 2014


Vladan Panković, Stevica Ðurović, Miodrag Krmar, Darko Kapor

Department of Physics, Faculty of Sciences, 21000 Novi Sad, Trg Dositeja Obradovića
4., Serbia, Gimnazija, 22320 Inđija, Trg slobode 2a, vladan.pankovic@ df.uns.ac.rs

PACS number: 03.50.De , 41.20. -q
Key words: Faraday's disc paradox, symmetry breaking

Abstract

In this work we realize a simple experimental procedure of the visual demonstration of remarkable Faraday's disc paradox. Precisely, we set up a tiny paper plane with a small lot of small iron nails distributed or "condensed" along some lines of the magnetic field above and nearly static cylindrical magnet upper end. In this way some lines of the magnetic field of mentioned static magnet become effectively visualized. Then, we rotate magnet around its symmetry axis and we simply observe what happen with visualized magnetic field lines. Definite result of the realized experiment is visualized magnetic field lines do not rotate at all in full agreement with Faraday's assumption. Moreover we experimentally study what happen with visualized magnetic field lines by translations of the magnet when symmetry surface gradually decreases or increase. Definite result of the realized experiment is that visualized magnetic field lines behave in full agreement with simply generalized Faraday's assumption that include corresponding characteristic symmetry breaking (and "phase transitions") phenomena. All this can be very useful for the experimental practice and a better understanding of the basic (electro)magnetic field concepts.

"Eprur si non-muove!"

1. Introduction

Well-known experiment of the Faraday's disc (including its numerous variations) [1]- [5] can be consequently considered as a procedure of the detection of the magnetic field (lines) characteristics of a rotating (around its symmetry axis) cylindrical magnet using non-visual, electromagnetic induction effects. (It is in some degree similar to the detection of the nuclear radiation using a non-visual detector, e.g. ionic chamber.) This experiment, as it has been assumed by Faraday, implies that by rotation of the cylindrical magnet around its characteristic symmetry axis magnetic field lines remain completely static. It can seem strange, moreover paradoxical, nevertheless all this is in full agreement with standard electro-dynamical laws (Faraday's induction law or, generally, Maxwell equations).

In this work we shall suggest and realize a simple (so simple that it can be realized practically in any elementary school during few minutes) procedure of the unambiguous visual detection of magnetic field (lines) characteristics of mentioned rotating cylindrical magnet. (It is in some degree similar to detection of the nuclear radiation using a visual detector, e.g. Wilson's cloud chamber.) Precisely, we shall set up a tiny paper plane with a lot of small iron nails with tops (or without tops, iron pellets, balls or even iron dust in more sophisticated versions of the experiment that will not be discussed explicitly here) distributed or "condensed" along some lines of the magnetic field above and nearly static cylindrical magnet upper end. In this way some lines of the magnetic field of mentioned static magnet will become effectively visualized. Then, we shall rotate magnet and we shall simply observe what will happen with visualized magnetic field lines. Definite result of the realized experiment is that visualized magnetic field lines do not rotate at all in full agreement with Faraday's assumption.

Moreover we shall experimentally study what happen with visualized magnetic field lines by translations of the magnet when symmetry surface gradually decreases or increase. Definite result of the realized experiment is that visualized magnetic field lines behave in full agreement with simply generalized Faraday's assumption that include corresponding characteristic symmetry breaking (and "phase transitions") phenomena. All this can be very useful for the experimental practice and a better understanding of the basic (electro)magnetic field concepts.

2. Simple visual demonstration of the Faraday's disc paradox

Let us describe more accurately our experimental set-up. The construction is rather simple consisting on three parts.

The first part is a cylindrical magnet positioned on the top part of cut-off conus so that axes of the magnet and conus coincide.

The second part is a thin, smooth, plane sheet of paper positioned a little bit above the upper part of the cylindrical magnet. The edges of the paper sheet are stretched and fixed on both sides by two statives.

The third part represents a small amount of small iron nails whose weight does not produce any significant curving of the paper sheet.

It is very important to be pointed out the following. Even tiny, paper does not admit a strong interaction between magnet and iron nails so that iron nails are not strictly fixed for magnet so that many forms of the eventual relative motion of the nails in respect to magnet can be unambiguously realized and observed.
The experiment is realized in two phases.

In the first phase, the magnet is stationary and the nails are distributed along some of the lines of magnetic field inside and outside the circle on the paper, corresponding to the top circle of the magnet. In this way, at least some of the magnetic lines of stationary magnet become effectively visualized. Within the circle, the nails are stabilized standing on their tops in the direction vertical to the surface of the circle. Outside the circle, the nails group in horizontal linear fragments directed towards the center. The distribution of the nails within and outside the circle should be chosen to be asymmetric and the lengths of linear fragments should be different, in order to make easier following the eventual rotation of visualized magnetic lines.

In the second phase of the experiment by manual action on the lower part of the conus, which also activates the magnet, they both begin to rotate around the symmetry axis by the corresponding small (angular) speed. One notices the following. All visualized the lines of the magnetic field, with smaller vibrations caused by the non-ideal manual rotation, do not rotate and in that sense remain static. The vibration effects clearly show that the absence of rotation is not caused by the friction between the nails and paper basis.

On the basis of realized experiment (which everybody can repeat very easy) it can be clearly and definitely concluded that during ideal rotation of cylindrical magnet around its symmetry axis, all its lines remain visibly motionless. It is in complete agreement with Faraday's assumption, however strange it might look.

3. Generalized Faraday's paradox and characteristic symmetry breakings by cylindrical magnet translations

Now we can realize some other experiment with practically the same experimental set- up. Namely, we can translate cylindrical magnet in a direction parallel to some diameter of the magnet circle at magnet basic area with relatively small speed and then we can see what will happen with visualized magnetic field lines.

The new experiment is realized in two phases again.

In the first phase, denote corresponding diameter of the circle of magnet at paper plane in the initial time moment with linear segment [A(0), B(0)]. Inside initial circle at paper plane we shall set up again inhomogeneously distributed few iron nails (some of which at heads and some of which at tops) so that their eventual translation by mentioned magnet translation can be simply observed. Outside of the initial circle, precisely at its circumference, at paper plane we shall set up more, homogeneously distributed over circumference, iron nails. Then any eventual motion of these nails (with or without appearance of the homogeneity distribution disturbation effects) in the paper plane, by mentioned magnet translation, can be simply observed.

In the second phase of the new experiment by manual action on the lower part of the conus, which also activates the magnet, they both begin to translate in mentioned direction with the corresponding small (translation) speed. In some time moment t initial magnet diameter, i.e. linear segment [A(0), B(0)] turns out in final magnet diameter, i.e. corresponding final linear segment [A(t), B(t)] at the translation direction. Firstly we can observe such situations when A(t) is inside and B(t) is outside the initial interval and later we can observe such situations when both A(t) and B(t) are outside the initial interval.

By realization of the experiment (which everybody can repeat very easy) one notices the following. All visualized the lines of the magnetic field inside initial circle remain static practically till moment of the touch with the final circle circumference. After this moment visualized magnetic field lines turn out outside final circle, i.e. at its circumference. Simply speaking, till touching moment, magnetic field nearly corresponding visualized static lines is locally symmetric in respect to the mentioned translation, while in touching moment this local symmetry becomes broken. All this seems as a "discontinuous phase transition" too.

On the other side, all visualized the lines of the magnetic field outside initial circle are "translated" in a complex way correspondingly to the translated magnet. Namely, outside of the final circle, precisely at its circumference, there is real distribution of the iron nails that have belonged to the initial circle (if we neglect .previously discussed effects of the local translation symmetry breaking and transition of some internal nails at the circumference). Meanwhile, final distribution of the iron nails along this final circumference is not more homogeneous. During translation time all nails at the circumference, right or left in respect to [A(t), B(t)], escape gradually from B(t) and tend toward A(t). (Single nail initially placed exactly in A(0) or B(0) point becomes by ideal translation appears correspondingly in A(t) or B(t) point.) In this way, during translation time, (small) vicinity of B(t) point holds less and less nails, while vicinity of A(t) point holds more and more nails. Metaphorically speaking, initial circle with "hair" and "bird" turns into final circle practically without "hair" and with very intensive "Chinese bird".

Vice versa, if we further realize inverse translation, in opposite direction, we again obtain a gradual return of the homogeneity of distribution of nails over circumference, moreover, after sufficiently long time interval, vicinity of A(t) point holds less and less nails, while vicinity of B(t) point holds more and more nails. All this seems as a "continuous phase transition" too.

Now we can simply generalize Faraday's assumption in the following way. By such mechanical motion of a magnet during which magnetic field in some area stand locally or globally symmetric in this area there is no motion of corresponding magnetic field lines.

4. Concluding remarks

In conclusion we can repeat and point out the following.

Firstly, it is very important to be pointed out the following. If in previously discussed experiment tiny paper plane is completely removed, small iron nails that visualize some magnetic field lines become strongly fixed for magnet and they move commonly with magnet. But then in different time moments the same iron nail visualizes different magnet field lines. It implies that here absence of the relative motion of the magnet in respect to the iron nails does not mean in any way absence of the relative motion of the magnet in respect to the magnet field lines (demonstrated definitely in mentioned experiment with paper).

Thus, in this work we realize a simple experimental procedure of the visual demonstration of remarkable Faraday's disc paradox. Precisely, we set up a tiny paper plane with a small lot of small iron nails distributed or "condensed" along some lines of the magnetic field above and nearly static cylindrical magnet upper end. In this way some lines of the magnetic field of mentioned static magnet become effectively visualized. Then, we rotate magnet around its symmetry axis and we simply observe what happen with visualized magnetic field lines. Definite result of the realized experiment is visualized magnetic field lines do not rotate at all in full agreement with Faraday's assumption. Moreover we experimentally study what happen with visualized magnetic field lines by translations of the magnet when symmetry surface gradually decreases or increase. Definite result of the realized experiment is that visualized magnetic field lines behave in full agreement with simply generalized Faraday's assumption that include corresponding characteristic symmetry breaking (and "phase transitions") phenomena. All this can be very useful for the experimental practice and a better understanding of the basic (electro)magnetic field concepts.

Acknowledgements

Authors are very grateful to Branko Marčeta, Milan Mrđen and Vojislav – Voja Božić "Sremac" for technical help.

References

[1] M. Faraday, Philos. Trans. R. Soc. (1832) 125
[2] D. E. Tilley, Am. J. Phys. 36 (1968) 458
[3] M. J. Crooks et al, Am. J. Phys. 46 (1978) 729 and references therein
[4] R. P. Feynman, R. B. Leighton, M. Sands, The Feynman Lectures on Physics Vol. 2, Chapter 17 (Addison-Wesley Publ. Inc., Reading, Massachusetts, 1964)
[5] F. Munley, Am. J. Phys. 72 (2004) 1478 and references therein

PICTURES

slika

Picture 1 – Experimental set-up

 

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Picture 2 – Visualized lines of the magnetic field standing static by magnet rotation

 

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