The parametric oscillations of an oscillator driven electromagnetically are presented. The oscillator is a conductive pipe hung from a spring, and driven by the oscillating magnetic field of a surrounding coil in the presence of a static magnetic field. It is an interesting case of parametric oscillations since the pipe is neither a magnet nor a ferromagnet, and because the driving and the damping forces are functions of the magnet-to-pipe distance. We develop an analytical model of the oscillator that leads to a new kind of Mathieu equation with nonlinear terms of third order in the oscillator position, and on the product of the squared position times the first derivative of the position function. We show how the oscillations evolve as the frequency is varied up to the saturation regime and present ample experimental evidence of the parametric nature of our oscillator. Because of its peculiarities and their advanced scientific and technological applications, parametric os...

The spatial variation in phase and the propagating wave-front of plane wave electromagnetic radiation are widely familiar text-book territory. In contrast, the developing amplitude and phase of radiation emitted by a dipole or multipole source generally receive less attention, despite the prevalence of these systems. There is additional complexity in such cases where, in consequence of retardation, the character and features significantly and progressively change as radiation propagates onwards, from the near-field and out towards the wave-zone. Readily developed analytical representations of the electric field, cast as a function of distance from the source, provide illuminating insights into the most prominent and distinctive properties of radiant electromagnetic emission. Graphical implementations and animations of the results prove particularly instructive in revealing the spatial form and temporal evolution of the emergent electromagnetic fields.

Double-exposure holographic interferometry is applied to measure the linear or longitudinal magnetostriction constant of a soft-ferrite rod. This high-accuracy measurement is done indirectly, by measuring the small rotations of a lever in contact with the rod using double-exposure holographic interferometry implemented with a robust arrowhead-shaped holographic setup. Ferrite devices are used in a large number of well-known technologies and hold a promise for more advanced applications, so the study of ferrites properties is therefore very important. The experiments and methods described here and the magnetic phenomena studied are suitable for an undergraduate project or an open-ended experiment.

This study shows physicists' discussions on the meaning of Faraday's law where situations involving extended conductors or moving contact points are particularly troublesome. We raise questions to test students' difficulties in applying Faraday's law in motional electromotive force phenomena. We suggest the benefit of analysing these phenomena when teaching Faraday's law in introductory physics courses at university. We are not implying that Faraday's law should be revised, but we do want to set the stage for careful rethinking regarding the meaning and application of each term of the law as it appears in traditional introductory courses.

In nonrelativistic quantum mechanics, the total (i.e. orbital plus spin) angular momentum of a charged particle with spin that moves in a Coulomb plus spin–orbit-coupling potential is conserved. In a classical nonrelativistic treatment of this problem, in which the Lagrange equations determine the orbital motion and the Thomas equation yields the rate of change of the spin, the particle's total angular momentum in which the orbital angular momentum is defined in terms of the kinetic momentum is generally not conserved. However, a generalized total angular momentum, in which the orbital part is defined in terms of the canonical momentum, is conserved. This illustrates the fact that the quantum-mechanical operator of momentum corresponds to the canonical momentum of classical mechanics.

In this paper, we describe how simple experiments realizable by using easily found and low-cost materials allow students to explore quantitatively the magnetic interaction thanks to the help of an Open Source Physics tool, the Tracker Video Analysis software. The static equilibrium of a ‘column’ of permanents magnets is carefully investigated by working on digital photos, while the anharmonic oscillations of a magnetic bar under the action of gravity and of magnetic repulsion are analysed by using a digital video. A detailed comparison between theoretical expectations and experimental results is discussed. We discuss how the magnetic force falls off with the distance between the permanent magnets following an inverse pth power law. Static and dynamic measurements of the force and of the periods for small amplitude harmonic oscillations yield an experimental value for p ≈ 2. The dynamical system is a good example of an anharmonic oscillator. The experiments need simp...

In this paper we discuss a pedagogical approach aimed at pointing out the role played by the Boltzmann factor in describing phenomena usually perceived as regulated by different mechanisms of functioning. Experimental results regarding some aspects of a chemical reaction and of the viscous flow of some liquids are analysed and described in terms of macroscopic variables whose temperature dependence is proportional to the Boltzmann factor. A description of a workshop implementing the approach in the framework of an undergraduate course for engineering education and some preliminary results about its pedagogical relevance are then reported.