In this article we describe an experimental learning path about electromagnetic induction which uses an Atwood machine where one of the two hanging bodies is a cylindrical magnet falling through a plexiglass guide, surrounded either by a coil or by a copper pipe. The first configuration (magnet falling across a coil) allows students to quantitatively study the Faraday–Neumann–Lenz law, while the second configuration (falling through a copper pipe) permits learners to investigate the complex phenomena of induction by quantifying the amount of electric power dissipated through the pipe as a result of Foucault eddy currents, when the magnet travels through the pipe. The magnet’s fall acceleration can be set by adjusting the counterweight of the Atwood machine so that both the kinematic quantities associated with it and the electromotive force induced within the coil are continuously and quantitatively monitored (respectively, by a common personal computer (PC) equipped with a webcam and by freely available software that makes it possible to use the audio card to convert the PC into an oscilloscope). Measurements carried out when the various experimental parameters are changed provide a useful framework for a thorough understanding and clarification of the conceptual nodes related to electromagnetic induction. The proposed learning path is under evaluation in various high schools participating in the project ‘Lauree Scientifiche’ promoted by the Italian Department of Education.
In this paper we present an experimental strategy to measure the micro power dissipation due to Foucault ‘eddy’ currents in a copper cylinder rolling on two parallel conductive rails in the presence of a magnetic field. Foucault power dissipation is obtained from kinematical measurements carried out by using a common PC webcam and video analysis done by means of software tools freely available within Windows operating system (Paint and Movie Maker). The proposed method allows us to experimentally discern the contribution to dissipation due to the velocity-independent rolling friction from that owed to the viscous-like friction emerging from complex electrodynamic interactions among eddy currents and the external magnetic field. In this way a microdissipation of some tens of µW is measured. The easily reproducible experimental setup, the simple implementation of data analysis and the discussion on various experimental approaches and strategies make the proposed activity highly significant for university undergraduates, since involved crucial skills can be efficiently strengthened.
The Galilean invariance of work–energy theorem, at an elementary mechanics level, has not been deeply discussed in the past, nor have its implications in connection with other fundamental mechanical laws been investigated. In this paper we give some further insight into the work–energy theorem, showing that its Galilean invariance implies the impulse theorem. We also introduce a formalism to determine temporal details of motion only by means of energetic considerations. Applications of the formalism are also presented, which are interesting both for graduates and for university undergraduates.
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Under some conditions, the method of images (well known in electrostatics) may be implemented in magnetostatic problems too, giving an excellent example of the usefulness of formal analogies in the description of physical systems. In this paper, we develop a quantitative model for the magnetic interactions underlying the so-called Geomag™ paradox and describe a quantitative experimental investigation to validate the model. The validity ranges of some approximations involved in this problem are quantitatively discussed and the advantages of a dimensionless formulation of the interaction are pointed out. This work offers many educational suggestions suitable for university students.
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