Foucault dissipation of a magnet falling through a copper pipe studied by means of a PC
audio card and webcam
Assunta Bonanno1, Giacomo Bozzo1,3, Michele Camarca1, Marisa Michelini2, Peppino Sapia1
1.
2.
3.
Physics Education Research Group, Physics Department, University of Calabria – Rende (CS) – Italy
Physics Education Research Group (URDF), University of Udine –Udine – Italy
bozzo@fis.unical.it
Abstract. In this paper we describe an experimental learning path on the
electromagnetic induction based on the original use of an Atwood machine to obtain
a controlled fall of a cylindrical magnet. Two different experimental setup are used:
i) magnet falling across a coil (allowing to quantitatively study the FaradayNeumann-Lenz law directly); ii) magnet falling across a copper pipe. This last
configuration allows to investigate complex induction phenomena, by quantitatively
determining power dissipation due to Foucault eddy currents, arising in the copper as
magnet travels through it. Both mechanical and electromagnetic aspects of the
phenomenon are continuously and quantitatively monitored by a common personal
computer (PC) equipped with a webcam, and a freely available specific software
allowing to employ PC as an oscilloscope through the audio card. Measurements
carried out when the various experimental parameters are changed provide a useful
framework for a thorough didactic discussion of the conceptual knots related to
electromagnetic induction. The proposed learning path is under evaluation in some
high school, within the Project “Lauree Scientifiche” promoted by the Italian
Department of Education.
1. Introduction
Experimental activity plays a crucial role in Physics Education research. Many researchers stressed
the importance of laboratory activities in learning process to increase student interest towards
Physics and to create connections between science knowledge and everyday world experience
(Bosio et al 2001, Bosio et al. 1997). Physics, in fact, is one of most difficult and boring school
subject in spite of its many everyday applications (Bonanno et al. 2009b). Hands-on and minds-on
activities can boost reasoning skills of students, through problem solving (Watts, 1983) and small
group collaborative work (Heron 2008 Meltzer and Manivannan 2002, Coletta et al. 2007), as well
as can effectively address the main student’s misconceptions if supported by appropriate
learning/teaching strategies. Student interest is enhanced by on-line measurements, who offer a
great support for experimental activity, since they allows to follow in real time the evolution of
phenomena and to perform quantitative investigations (Gervasio et al. 2009, Bonanno et al. 2010).
On-line acquisition systems, cheap and easy to use, capture student attention, allowing them to
understand contents and to improve their own knowledge. However, although many not expensive
on-line acquisition devices are commercially available, many schools had great difficulties to buy
them. Furthermore, students cannot repeat these experiences at home, although they are easily made
at school, because acquisition systems and data analysis software are not accessible for free.
On the other side, international literature has clearly identified the main difficulties encountered by
learners in dealing with conceptual challenges of electromagnetic induction (Michelini and Viola
2007, Stefanel 2008, Bonanno et al. 2010), especially in facing the role of magnetic field flux and
its time variation (Maloney 2001, Thong 2008, Galili 1997, Michelini 2008, Michelini 2009,
Bonanno et al. 2010). In this context we proposed, in MPTL 2009 Conference (Bonanno et al.
2010), an on-line experiment in which real time graphs allow to face the conceptual knots relative
to induced currents in electromagnetic phenomena, stressing the role of magnetic field flux
variation. Anyway, during our didactic experimentation, we encountered several difficulties to
introduce data acquisition system in schools because of their limited economic resources.
In this context, to overcome described troubles, we propose here an improved version of the
experimental set up presented at the MPTL 2009 Conference, specifically designed to address some
conceptual knots related to energy conversion (from mechanical to electrical), in addition to those
concerning the role of magnetic flux variation in electromagnetic induction. The need for such an
improvement has been suggested to us by our didactical experimentation, that has shown as
conceptual knots related to energy conversion remained not fully clarified when the activity is
specifically and exclusively focused on the magnetic flux variation (Bonanno et al. 2009a).
Figure 1: Experimental set up: 1) Atwood machine;
2) falling magnet; 3) counterweight; 4) inextensible
string, 5) home-made coil, 6) support pole.
The coil is connected to the microphone plug-in of
the PC audio card through a clipper circuit
(employing 4 diodes 1N4007 connected as in the
figure), to protect the card from possible voltage
spikes. The clipper threshold is about 1.3 V.
2. Experimental set up with Atwood Machine
Proposed experimental learning path is based on an improved Atwood machine holding at one end a
cylindrical magnet falling through a Plexiglas guide (Figure 1). This guide acts as a mechanical
support for either a coil (Figure 2) or a conducting copper pipe through which the magnet can fall.
In this way, two experimental configurations are possible, each aimed to address complementary
conceptual knots concerning electromagnetic induction phenomena. A first configuration, featured
by the guide surrounded with an induction coil, lets the magnet falling through the coil with
controlled acceleration, so that a quantitatively study of the induction law is directly allowed. In the
other experimental arrangement the guide is surrounded by a copper pipe, whose length may be
determined by the experimenter. In this way, kinematic study on the falling magnet permits the
quantitative determination of power dissipation due to Foucault eddy currents (arising in the copper
as magnet travels through it) and a consequent deeper insight into the complex induction
phenomena. In both configurations, magnet acceleration may be set at wish by adjusting Atwood
machine’s counterweight.
One of the strengths of proposed experimental set up resides in the fact that both aspects of the
phenomenon under investigation (mechanical and electromagnetic, as regards respectively, the
motion and the induction) are continuously and quantitatively monitored through a common home
PC, used as a low cost acquisition system. In fact, a freely available specific software 1, permits to
1
“Visual Analyzer Project”, Tor Vergata University, Italy. On line at the URL: http://www.sillanumsoft.org/
employ the PC as an oscilloscope, via the audio card, so that the signal induced in the coil (while
magnet crosses it) can be easily acquired. Similarly, the use of a webcam (640x480 pixel resolution,
25 frame per second – fps – speed), connected via USB to the PC, allows to perform the
quantitative study of the motion, as elsewhere described by us (Bonanno et al. 2011).
The proposed activity provides students with the opportunity to perform quantitative experiments
aimed, among other things, to: i) strengthen skills concerning data analysis; ii) get a deeper
comprehension of important phenomena based on electromagnetic induction. In fact, the
experiment with the coil is designed to guide to a correct analysis and comprehension of conceptual
knots related to induced current, stressing the role of magnetic field flux variation. The experiment
with the copper pipe set up allows students to quantitatively estimate Foucault force value and its
dissipative effects. Both settings use free software available in internet or in all domestic PC so that
students can utilize the PC audio card as a common data acquisition card, effectively supported by
the simultaneous use of the webcam.
2. 1. Magnet falling through a coil
In this configuration (Figures 1 and 2) the magnet falls (with adjustable acceleration) through a coil
and the electric signal induced in it is acquired and digitized using the audio-card-based acquisition
system previously described. In this way, the Faraday law may be quantitatively studied by
analyzing the Electromotive Force (EMF) as a function of time. As can be seen in Figure 2, when
the magnet approaches to the coil, there is an increasing magnetic field flux and the induced current
produces a magnetic field opposing to this increase, so that a repulsion will be produced between
the magnet and the coil. As magnet enters the coil (Figure 2a), a peak is observed in the signal since
the magnetic field is stronger at the poles. Until the second pole has entered the coil (Figure 2b), the
magnetic field flux through it is nearly constant. Consequently in this temporal interval the induced
tension almost vanishes. When the second pole crosses the coil (Figure 2c), there is a decrease in
the magnetic field flux; therefore the induced tension is sign-reversed with respect to the previous
situation.
It’s very interesting to observe the difference between modules of peak amplitudes (Figure 2d)
when the coil is crossed by, respectively, the bottom or the top pole of the magnet. In fact, since
magnet’s motion is uniformly accelerated, the magnet entry speed is smaller than the exit one and,
consequently, magnetic field flux variation at the way in of the coil is slower than at its way out.
The software we used allows to perform analysis of the electrical signal in a very simple, though
didactically significant, manner. For example, proposed method permits to investigate the
dependence of the peak amplitude and width on the magnet crossing-speed, and so on fall height. In
this context, we propose to perform this type of analysis by using a video editing program
(Windows Movie Maker – Figure 3) available in all domestic PC. The video acquisition by a
webcam permits to analyze the time evolution of the magnet position and speed through the video
frames saved as snapshots (Bonanno et al. 2011).
Movie Maker video acquisition captures a series of images (frames) of the magnet falling motion in
a fixed time interval. Analyzing the magnet distance from starting position, it is possible to derive
empirically the system acceleration a by using the equation of uniformly accelerated motion
𝑥(𝑡) = 12𝑎 ∙ 𝑡 2 . This allows to obtain the magnet speed (for each frame), according to the law
𝑣(𝑡) = 𝑎 ∙ 𝑡. We use a simple image editing program (like Paint) to estimate the distances traveled
by the magnet in terms of pixel numbers (Figure 4). A fixed reference length included in all the
acquired images can be used in order to convert distances from pixels to centimeters.
Figure 2: magnet enters (a), crosses (b), leaves (c) the coil. The graph (d)
shows the difference between modules of peak amplitude.
Figure 3: Data analysis
using Windows Movie
Maker.
Figure 4: The yellow ruler sets the
scale: its length (31.3 cm)
corresponds to 108 pixels. Each
pixel is equal to 0.29 cm.
As concerns the time scale, we point out that the interval between successive frames (1/25 sec) can
be easily deduced from the webcam rated frame-speed (25 fps). This nominal time step has been
checked by taking a movie of a running digital chronometer and then verifying that the difference
between the times marked by the clock in successive frames equals 1/25 sec.
Plotting the distance traveled by the magnet versus time, it’s possible to observe a parabolic trend
(Figure 5), where the parabola axis of symmetry is parallel to the distance-axis with the vertex at
(0,0), as expected by equation of motion 𝑥(𝑡) = 12𝑎 ∙ 𝑡 2 .
Figure 5: an example of (a) distance covered by magnet vs time and (b)
distance covered by magnet vs time square.
We can obtain the acceleration from the distance-versus-time-square graph (Figure 5), where line
𝑚
slope is equal to 12𝑎 (in this example, experimental acceleration value is: 𝑎 = 0,872 𝑠2 ).
This experimental value can be compared with the theoretically predicted one (atheor.=1,028 m/s2),
which can be easily obtained by elementary mechanics. Despite theoretical approximations (friction
forces are neglected and momentum of inertia of a uniform disk has been considered), the
experimental value is not too different from the theoretical one (about 15%).
At this point we can calculate the speed value for each instant, using the second equation of motion
𝑣(𝑡) = 𝑎 ∙ 𝑡, in particular when magnet enters or leaves the coil (Figure 6).
Figure 6: Magnet speed vs time obtained from the webcam video analysis.
Marked points refer to the instants when magnet enters and leaves the coil.
2. 2 Magnet falling through a Copper Pipe
The second experimental set up allows to highlight dissipative effects due to Foucault forces, by
dropping a magnet through a copper pipe of various length 2. This experiment allows, among other
things, to achieve the didactical goal of clarifying the difference between accelerated motion and
motion at constant velocity.
Figure 7 shows a typical experimental plot in which we can distinguish three different regimes: a)
magnet falls with a constant acceleration (until it enters the copper pipe), b) magnet moves with
constant speed through the copper pipe, c) magnet falls again with a constant acceleration (equal to
that one of the first zone) as it exits the copper pipe.
Figure 7: Magnet position vs time; we can distinguish three different regimes: the first in
which the magnet falls with a constant acceleration, the second in which the magnet moves
with constant speed through the copper pipe, the third in which the magnet falls again with a
constant acceleration.
3. Data analysis
A thorough analysis of data acquired with the prosed Atwood machine, in both described
configurations, provides the context for addressing a series of educationally meaningful topics
pertaining conceptual knots above mentioned. In the following we show some significant example
of possible data analysis.
3.1 Magnet falling through a Coil
The software we used gives opportunities to perform the analysis of electrical signal induced in the
coil, when it’s crossed by the magnet. At this regard, an interesting observation is that when the
falling height decreases peak amplitude decreases too, while peak width increases (Figure 8). The
same behavior for peck amplitude and width is observed when Atwood machine’s counterweight is
increased, so that falling acceleration is correspondingly reduced (Figure 9). Both behaviors may be
readily connected to the dependence on magnet crossing speed of inductive effects, since the time
2
MOSEM2 Project – online at the URL: http://supercomet.no/gb/MOSEM2
derivative of magnetic flux (which determines the signal amplitude) is directly related to magnet
speed (and acceleration).
It follows from the above examples that a careful area analysis has a high educational value. Indeed,
the fact that total area under the EMF-vs-time plot is zero has the deep meaning of the magnetic
monopole non-existence. Such an analysis may be effectively performed by using Microsoft Excel
software.
Figure 10 shows that the area under the positive (or negative) peak remains constant (with respect to
the variation of falling height or value of counterweights), while Figure 11 highlights that total
magnetic field flux variation is nearly to zero.
Figure8: When the falling height decreases peak amplitude decreases while
peak width increases (using a fixed counterweight).
Figure 9: When the small weights increase peak amplitude decreases while
peak width increases (at a fixed falling height).
Figure 10: Area Analysis (flux variation analysis): the area under the positive (or
negative) peak remains constant (with respect to the variation of falling height or small
weights).
Figure 11: Total Area (i.e. total magnetic field flux variation) is nearly to zero.
3.2 Magnet falling through a Copper Pipe
Finally, we can show the effects of electromagnetic induction by dropping a magnet through a
copper pipe of various length in order to highlight dissipative effects due to Foucault force. Using
this set up, we obtain the space-time diagram of the motion (Figure 12) and analyze magnet speed
and time needed to cross the copper pipe.
Figure 12: typical trend of magnet position versus time in which we can distinguish
three regimes (a); Through Movie Maker analysis it’s possible to calculate speed value
of second regime and acceleration value of first and third regimes (b).
Analysis of recorded motion movies, performed by employing Movie Maker, permits highlighting
three motional regimes in the magnet’s fall, allowing in particular to determine the speed value of
second (uniform motion) regime, and acceleration value of first and third ones (Figure 12.b). In this
way, we achieve the didactical goal of clarifying the difference between an accelerated motion and
a motion at constant velocity. By using pipes of different lengths, we can observe that the various
space-time diagrams are different only in second regime duration (Figure 13), i.e., that
characterized by a constant falling speed, reached because of the dissipative effects due to the
viscous-like force arising from the electrodynamical interactions between the magnet’s magnetic
field and the Foucault eddy currents induced in the copper pipe by the passage of the magnet itself.
Figure 13: Comparison between trends of magnet position for different copper pipes
shows that relative graphs are different only in second regime duration.
Finally we can easily determine the dissipative effect due to Foucault forces, when a stationary
regime is reached. In fact, noting that in this regime the braking Foucault force is given by the
difference between Atwood machine’s weights, by appropriately substituting numerical values we
easily obtain:
𝐹𝐹𝑜𝑢𝑐 = (𝑚1 − 𝑚2 )𝑔 = 5,8 × 10−2 𝑁
Similarly, power dissipation due to Foucault force may be obtained multiplying by the falling
speed:
𝑃𝐹𝑜𝑢𝑐 = 𝐹𝐹𝑜𝑢𝑐 ∙ 𝑣 = 7,5𝑚𝑊
4. Conclusions
In this paper we presented an experimental learning path on the electromagnetic induction, based
on an improved version of the Atwood machine. Two different forms of the experimental set up
have been proposed. The first one contemplates the falling of a magnet through a coil and allows
students to understand Faraday-Neumann-Lenz law. In the second set up the magnet falls through a
conductor pipe and the energy dissipation due to Foucault eddy currents may be quantitatively
investigated. Both settings use high tech (though low cost and widely available) technological
devices, such as webcam and PC audio card, and employ freely available software allowing
students to utilize PC as an oscilloscope. Proposed activity provides students the opportunity to
perform quantitative experiments useful, among other things, in developing such a fundamental
skills as data analysis capability and competence in instrument calibration. The activity, moreover,
allows a deeper interpretation of an important phenomenon based on electromagnetic induction, as
the Foucault eddy currents. Real time graphs of time depending phenomena play a central role in
this didactical activity, focusing students attention on the role of several parameters (coil number,
falling height and employed weights) characterizing the Atwood machine. In this regard, we stress
the advantage of on-line acquisition, also from a didactical point of view, since it allows
students/experimenters to have an immediate feedback on the effects of parameter variation.
Moreover the brainstorming discussion showed how pupils finally and successfully linked induced
current to the magnetic flux variation through the coil. A typical student observation was: “current
appears when spaghetti number through the coil increase or decrease in time”, where “spaghetti”
obviously are magnetic field lines.
References
Bonanno A, Bozzo G, Camarca M, and Sapia P 2009a. How students interpret a simple situation of induction
phenomena, GIREP 2009 Conference – To be published.
Bonanno A, Bozzo G, Camarca M, Oliva A and Sapia P 2009b. Four physics jar, Il Nuovo Cimento 31 601-15 (2009).
Bonanno A, Bozzo G, Camarca M, and Sapia P 2010. An on line experiment on electromagnetic induction, in:
Proceedings of the “Multimedia in Physics Teaching and Learning International Conference”, MPTL 14, Udine
(Italy) September 23-35 2009.
On line at the URL: http://www.fisica.uniud.it/URDF/mptl14/contents.htm
Bonanno A, Bozzo G, Camarca M, and Sapia P 2011. Foucault dissipation in a rolling cylinder: A webcam quantitative
study, European Journal of Physics, in press (2011).
Bosio S, Michelini M, Pugliese J S, Sartori C and Stefanel A 2001. A research on conceptual change processes in the
context of an informal educational exhibit, in: Research in Science Education in Europe: the Picture Expands,
Edited by Bandiera M, Caravita S, Torracca E and Vicentini M (Rome, 2001).
Bosio S, Capocchiani V, Mazzadi M C, Michelini M, Pugliese S, Sartori C, Scillia M L and Stefanel A 1997. Playing,
experimenting, thinking: exploring informal learning within an exhibit of simple experiments, in: New Ways of
Teaching Physics, Edited by Oblac S. et al. (ICPE GIREP Book, Ljubjiana, 1997).
Bosio S, Capocchiani V, Michelini M, Santi L 1996. Computer on-line to explore thermal properties of matter, in:
Teaching the Science of Condensed Matter and New Materials , GIREP - ICPE Book, Forum 351 (1996).
Coletta V P, Phillips A A and Steinert J J 2007. Interpreting force concept inventory scores: Normalized gain and SAT
scores. Phys. Rev. ST Phys. Educ. Res. 3 – 010106 (2007).
Galili I and Kaplan D 1997. Changing approach in teaching electromagnetism in a conceptually oriented introductory
physics course. Am. J. Phys. 65 (7) 657-68
Heron P L R 2008. Research as a guide for the development and validation of curriculum: Examples in the context of
thermal physics. In: Proceedings of GIREP 2008 International Conference, to be published.
Gervasio M, Michelini M and Viola R 2009. Sensors as extension of senses via USB: three case studies on thermal,
optical and electrical phenomena. To be published in the proceedings of Konferencja Laboratoria Fizyczne
Wspomagane Komputerovo, Torun, Poland, 4-6/12/2008.
Maloney D P, O’Kuma T L, Hieggelke C J and Van Heuvelen A 2001. Surveying students’ conceptual knowledge of
electricity and magnetism. Phys. Educ. Res., Am. J. Phys. Suppl. 69 (7) S12-23 (2001).
Meltzer D E and Manivannan K 2002. Transforming the lecture-hall environment: The fully interactive physics lecture.
Am. J. Phys. 70 639 (2002).
Michelini M, Santi L, Stefanel A 2009. On line data acquisition experiments and modeling on electromagnetic
induction with coil and magnet. In: the MOSEM2 Project – Workshop 4 in MPTL14 (University of Udine) to be
published.
Michelini M and Viola R 2008. A proposal for a curricular path about electromagnetic induction. In: Proceedings of
GIREP 2008 International Conference, to be published.
Michelini M and Viola R 2007. Un laboratorio didattico per future insegnanti di scuola primaria sui nodi di
apprendimento dei fenomeni magnetici ed elettromagnetici. Atti del XLVI Congresso Nazionale A.I.F.- La Fisica
nella Scuola, XL, suppl. n. 3.
Stefanel A 2008. Disciplinary knots and learning problems in electromagnetism. In: Frontiers of Fundamental and
Computational Physics, 9th International Symposium, Edited by Sidharth B. G., Honsell F., Sreenivasan K., De
Angelis A. (American Institute of Physics, Melville, New York) 231-35.
Watts D M 1983. Some alternative views of energy, Phys. Educ. 18 213 (1983).
Thong W M and Gunstone R. 2008. Some Student Conceptions of Electromagnetic Induction, Res. Sci. Educ. 38 31-44
(2008).