Table of contents

A moderate-cost experimental setup is presented to help students to understand some qualitative and quantitative aspects of eddy currents. The setup operates like an eddy current brake, a device commonly used in heavy vehicles to dissipate kinetic energy by generating eddy currents. A set of simple experiments is proposed to measure eddy current losses and to relate them to various relevant parameters. Typical results for each of the experiments are presented, and comparisons with theoretical predictions are included. The experiments, which are devoted to first-year undergraduate students, deal also with other pedagogically relevant topics in electricity and magnetism, such as basic laws, electrical measurement techniques, the sources of the magnetic field and others.

We describe a simple experiment intended for didactic laboratory vacuum classes of undergraduate courses, using a residual gas analyser (RGA): the determination of the natural abundance of the different isotopes of a given element in a gas sample. In addition to the understanding of the RGA operation and handling principles, the experiment allows the students to perform direct quantitative measurements of isotopic abundances and compare with the results tabulated in the literature. As an example, sets of measurements are presented for xenon and neon using a quadrupole mass spectrometer. The experimental results obtained are in good agreement with the values presented in the literature.

This paper describes a simple laboratory measurement for measuring the Earth's magnetic induction field by means of a low cost experimental solution.

The optical properties of gradient index optical fibre are described as the basis for an undergraduate experiment. Its imaging ability is demonstrated by results obtained by two of the authors during their final year undergraduate research projects.

We study the motion of a quantum charged particle, constrained on the surface of a cylinder, in the presence of a radial magnetic field. When the spin of the particle is neglected, the system essentially reduces to an infinite family of simple harmonic oscillators, equally spaced along the axis of the cylinder. Interestingly enough, it can be used as a quantum Fourier transformer, with convenient visual output. When the spin-1/2 of the particle is taken into account, a non-conventional perturbative analysis results in a recursive closed form for the corrections to the energy and the wavefunction, for all eigenstates, to all orders in the magnetic moment of the particle. A simple two-state system is also presented, the time evolution of which involves an approximate precession of the spin perpendicularly to the magnetic field. A number of plots highlight the findings while several three-dimensional animations have been made available on the web.

The discretized Schrödinger equation is one of the most commonly employed methods for solving one-dimensional quantum mechanics problems on the computer, yet many of its characteristics remain poorly understood. The differences with the continuous Schrödinger equation are generally viewed as shortcomings of the discrete model and are typically described in purely mathematical terms. This is unfortunate since the discretized equation is more productively viewed from the perspective of solid-state physics, which naturally links the discrete model to realistic semiconductor quantum wells and nanoelectronic devices. While the relationship between the discrete model and a one-dimensional tight-binding model has been known for some time, the fact that the discrete Schrödinger equation admits analytic solutions for quantum wells has gone unnoted. Here we present a solution to this new analytically solvable problem. We show that the differences between the discrete and continuous models are due to their fundamentally different bandstructures, and present evidence for our belief that the discrete model is the more physically reasonable one.

We have developed an applet presentation showing different structures of a nematic liquid crystal confined to a thin transparent plan-parallel cell. The nematic structures possessing single defects or their pairs may be studied. The corresponding interference textures are shown simulating the polarization optic microscopy experiment. Several parameters defining the experimental set-up can be interactively varied enabling observation of subsequent changes in the interference pattern within a reasonable real time. The basic physics of liquid crystal defects necessary for understanding the limitations of the applet presentation is given.

Deformation quantization (sometimes called phase-space quantization) is a formulation of quantum mechanics that is not usually taught to undergraduates. It is formally quite similar to classical mechanics: ordinary functions on phase space take the place of operators, but the functions are multiplied in an exotic way, using the ⋆-product. Here we attempt a brief, pedagogical discussion of deformation quantization, which is suitable for inclusion in an undergraduate course.

The phenomenon of parametric resonance is explained and investigated both analytically and with the help of a computer simulation. Parametric excitation is studied for the example of the rotary oscillations of a simple linear system—mechanical torsion spring pendulum excited by periodic variations of its moment of inertia. Conditions and characteristics of parametric resonance and regeneration are found and discussed in detail. Ranges of frequencies within which parametric excitation is possible are determined. Stationary oscillations at the boundaries of these ranges are investigated. The simulation experiments aid greatly an understanding of basic principles and peculiarities of parametric excitation and complement the analytical study of the subject in a manner that is mutually reinforcing.

We discuss a couple of simple quasistatic electromagnetic systems in which the density of electromagnetic linear momentum can be easily computed. The examples are also used to illustrate how the total electromagnetic linear momentum, which may also be calculated by using the vector potential, can be understood as a consequence of the violation of the action–reaction principle, because a non-null external force is required to maintain constant the mechanical linear momentum. We show how one can avoid the divergence in the interaction linear electromagnetic momentum of a system composed by an idealization often used in textbooks (an infinite straight current) and a point charge.

Particle motion in a periodic potential is well known as the Kronig–Penney (KP) problem. Another physically meaningful structure is a periodic system that supports two kinds of particles that interact only at the interfaces (IF) of the system, leading to a coupled KP problem. Here, this nontrivial extension of the KP problem is solved analytically and insights are drawn about the resulting band structure, the possibility of IF bound states, and competition between size quantization and carrier localization at IFs, and wavefunction hybridization.

Some didactic aspects of the problem of writing Maxwell's equations independently of the unit systems are presented. In the case of the equations for the electromagnetic field in a medium it is argued that only two conventional constants are necessary.

The simple derivation of the planetary orbit described recently by Bringuier is related to previous publications in this journal that deal with the orbital motion and circular hodograph in the velocity space.

The full text of this article is available in the PDF provided.