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SIMPLE VISUAL DEMONSTRATION OF THE FARADAY’S DISC PARADOX

Created: Tuesday, 25 March 2014

Vladan Panković, Stevica Ðurović, Miodrag Krmar, Darko Kapor

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

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

 

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 will 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. All this can be very useful for the students for the experimental practice and a better understanding of the basic (electro)magnetic field concepts.

"Eprur si non-muove!"

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 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 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. All this can be very useful for the students for the experimental practice and a better understanding of the basic (electro)magnetic field concepts.
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.
Finally, 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)..
In conclusion we can repeat and point out the following. 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 will 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. All this can be very useful for the students for the experimental practice and a better understanding of the basic (electro)magnetic field concepts.

Authors are very gratiful to Branko Marčeta and Milan Mrđen for tehnical 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

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