Table of contents

TIn the autumn of 2010 I became the Editor-in Chief of European Journal of Physics (EJP). EJP is a place for teachers, instructors and professors to exchange their views on teaching physics at university level and share their experience. It is general opinion that no good research is possible without connection with good, high-quality teaching, at the university level in particular. Therefore excellence in physics teaching is important to the physics community. European Journal of Physics is proud of its contribution to achieving this goal.

As Editor-in-Chief, I will continue to work to this general objective of the journal. We will publish articles on specific topics in physics, stressing originality of presentation and suitability for use in students'laboratories, lectures and physics teaching in general. We will also publish more pedagogical papers presenting the achievements of particular teaching methods. In addition, we will continue to publish special sections on particular areas of physics, as well as the annual special section on physics competitions.

European Journal of Physics is in good shape. Due to the work of the previous editors and the publisher, the readership is high and growing steadily, and many excellent papers are being submitted and published. I hope that this positive trend for the journal will continue, and I will do my best to keep to this high standard.

A few words about myself. I work in the Institute of Physics in Warsaw, Poland. My main research interests are in theoretical quantum optics and I have published about 80 research papers on this topic. For many years I was involved in teaching physics at university and in high school. I am a co-author of a textbook on physics for high-school students and of a problem book in quantum mechanics. For the last ten years, I have been involved in the International Physics Olympiad and over the last few years I have been a member of the Editorial Board of European Journal of Physics.

The aim of this study is to investigate pre-service teachers' understanding of and difficulties with some core concepts in the special theory of relativity. The pre-service teachers (n = 185) from the Departments of Physics Education and Elementary Science Education at Dokuz Eylul University (in Turkey) participated. Both quantitative and qualitative research methods were used in this study. Students' understanding of and difficulties with core elements (time, length, mass and density) were tested using a paper-and-pencil questionnaire (including four questions) and in-depth interviews after the instruction of related modern physics topics. The analyses of the collected data were based on quantitative and qualitative techniques. The results indicate that pre-service teachers at different academic levels have specific and considerable difficulties with proper time, time dilation, proper length, mass and relativistic density concepts. In this paper, the conclusions of the study and implications for physics teaching are discussed.

The logical structure of classical thermodynamics is presented in a modern, geometrical manner. The first and second law receive clear, operatively oriented statements and the Gibbs free energy extremum principle is fully discussed. Applications relevant to chemistry, such as phase transitions, dilute solutions theory and, in particular, the law of mass action, are also addressed in a very detailed and novel manner. The material is best suited to graduate level students and professors, and it brings classical thermodynamics closer to other branches of university physics where geometry plays a key role.

The requirement of rotational invariance for lattice potential energies is investigated. Starting from this condition, it is shown that the Cauchy relations for the elastic constants are fulfilled if the lattice potential is built from pair interactions or when the first-neighbour approximation is adopted. This is seldom recognized in widely used solid-state textbooks. Frequently, pair interaction is even considered to be the most general situation. In addition, it is shown that the demand of rotational invariance in an infinite crystal leads to inconsistencies in the symmetry of the elastic tensor. However, for finite crystals, no problems arise, and the Huang conditions are deduced using exclusively a microscopic approach for the elasticity theory, without making any reference to macroscopic parameters. This work may be useful in both undergraduate and graduate level courses to point out the crudeness of the pair–potential interaction and to explore the limits of the infinite-crystal approximation.

This work explores the concept of dissipative work and shows that such a kind of work is an invariant non-negative quantity. This feature is then used to get a new insight into adiabatic irreversible processes; for instance, why the final temperature in any adiabatic irreversible process is always higher than that attained in a reversible process having the same initial state and equal final pressure or volume. Based on the concept of identical processes, numerical simulations of adiabatic irreversible compression and expansion were performed, enabling a better understanding of differences between configuration and dissipative work. The positive nature of the dissipative work was used to discuss the case where the dissipated energy ends up in the surroundings, while the invariance of such work under a system–surroundings interchange enabled the resulting modification in thermodynamical quantities to be determined. The ideas presented in this study are primarily intended for undergraduate students with a background in thermodynamics, but they may also be of interest to graduate students and teachers.

The capillary rise/fall of a liquid within a thin capillary tube is described by the well-established Jurin's law. The liquid reaches an equilibrium height/depth as the capillary pressure is balanced by the hydrostatic pressure. When the adhesion force at the three-phase contact line is counteracted by the liquid weight, the liquid column also stabilizes. Both descriptions evidently coincide although they are based on different physical quantities. Most undergraduate textbooks do not mention why these two routes draw two identical results; besides, the proofs become conceptually incorrect. We review the underlying ideas in Jurin's law and the two possible derivations.

Understanding students' prior beliefs in nuclear physics is a first step towards improving nuclear physics instruction. This paper describes the development of a diagnostic survey in nuclear physics covering the areas of radioactive decay, binding energy, properties of the nuclear force and nuclear reactions, that was administered to students at two institutions in a pre- and post-test design. The pre-test was given in a free-text entry format, with responses being used to develop a multiple-choice version that was given as a post-test. We performed statistical tests to evaluate the reliability and discriminatory power. Students' reasoning comments and rated certainties in their responses were used to determine students' misconceptions. We give details of misconceptions in the areas of radioactive decay, binding energy and nuclear density, and discuss possible underlying reasons for these misconceptions.

It is shown how the time-dependent Schrödinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton–Jacobi equation of classical mechanics. Schrödinger's own published derivations of quantum wave equations, the first of which was also based on the Hamilton–Jacobi equation, are also reviewed. The derivation of the time-dependent equation is based on an a priori assumption equivalent to Feynman's dynamical postulate. de Broglie's concepts of 'matter waves' and their phase and group velocities are also critically discussed.

This paper deals with the study of a toy CD hovercraft used in the fluid mechanics course for undergraduate students to illustrate the lubrication theory described by the Stokes equation. An experimental characterization of the toy hovercraft (measurements of the air flow value, of the pressure in the balloon and of the thickness of the air film under the hovercraft) allows us to evaluate a reduced Reynolds number R*. Since R* < 1, it is possible to simplify the Navier–Stokes equation that is reduced to the Stokes equation, on the basis of the lubrication theory. The pressure gradient in the air flow is calculated, allowing us to establish the lifting force applied on the toy hovercraft. In addition, these results are applied to a larger scale hovercraft.

We propose an analytic solution to the problem of the mechanical paradox consisting of a sphere rolling upwards on two diverging inclined guides as devised by Gardner. The presence of an unstable equilibrium point is highlighted and the analytic solution is found by means of elementary calculus concepts.

Marcella has presented a straightforward technique employing the Dirac formalism to calculate single- and double-slit interference patterns. He claims that no reference is made to classical optics or scattering theory and that his method therefore provides a purely quantum mechanical description of these experiments. He also presents his calculation as if no approximations are employed. We show that he implicitly makes the same approximations found in classical treatments of interference and that no new physics has been introduced. At the same time, some of the quantum mechanical arguments Marcella gives are, at best, misleading.

The spin of a top can be regarded as a fast variable, coupled to the motion of the axis which is slow. In pure precession, the rotation of the axis round a cone (without nutation), can be considered as the result of a reaction from the fast spin. The resulting restriction of the total state space of the top is an illustrative example, at graduate-student level, of the general dynamical concept of the slow manifold. For this case, the slow manifold can be calculated exactly, and expanded as a series of reaction forces (of magnetic type) in powers of slowness, corresponding to a modified precession frequency. The forces correspond to a series for the Hannay angle for the fast motion, describing the location of a point on the top.

The Hamilton action principle, also known as the principle of least action, and Lagrange equations are an integral part of intermediate and advanced undergraduate mechanics. Although the Hamilton principle is oft stated as 'the action for any nearby trial world-line is greater than the action for the classical world-line', the landscape of action in the space of world-lines is rarely explored. Here, for three common problems from introductory physics—a free particle, a uniformly accelerating particle, and a simple harmonic oscillator—we present families of trial world-lines, characterized by a few parameters, that evolve continuously from their respective classical world-lines. With explicit analytical expressions available for the action, they permit a graphical visualization of the action landscape in the space of nearby world-lines. Although these trial world-lines form only a subset of the space of all nearby world-lines, they provide a pedagogical tool that complements the traditional Lagrange equation approach. This tutorial is aimed at advanced undergraduate physics students.

The principle of equivalence was the first vital clue to Einstein in his extension of special relativity to general relativity, the modern theory of gravitation. In this paper we investigate in some detail students' understanding of this principle in a variety of contexts, when they are undergoing an introductory course on general relativity. The tool of assessment is a diagnostic questionnaire administered to a group of 30 senior undergraduates going through the course. The analysis of responses reveals a number of significant conceptual vulnerabilities in several aspects of the topic. The most important among these is related to the notion of an inertial frame that follows naturally from the principle of equivalence.

On the occasion of the laser's 50th anniversary, we performed a modern Fizeau experiment, measuring the speed of light with a laser beam passing over the city centre of Marseille. For a round trip distance of almost 5 km, the measurement has reached an uncertainty of about 10⁻⁴, mainly due to atmospheric fluctuations. We present the experimental and pedagogical challenges of this brilliant outreach experiment.

In a first study of thermoelastic waves, such as in the textbook of Landau and Lifshitz, one might at first glance understand that when the given period is very short, waves are isentropic because heat conduction does not set in, while if the given period is very long, waves are isothermal because there is enough time for thermalization to be thoroughly accomplished. When one pursues the study of these waves further, by the mathematical inspection of the complete thermoelastic wave equation one finds that if the period is very short, much shorter than a characteristic time of the material, the wave is isothermal, while if it is very long, much longer than the characteristic time, the wave is isentropic. One also learns that this fact is supported by experiments: at low frequencies the elastic waves are isentropic, while they are isothermal when the frequencies are so high that can be attained in few cases. The authors show that there is no contradiction between first-glance understanding and the mathematical treatment of the elastic wave equation: for thermal effects very long periods are so short and very short periods are so long.

We experimentally studied the restoring force of a length of stretched elastic cord. A simple analytical expression for the restoring force was found to fit all the experimental results for different elastic materials. Remarkably, this analytical expression depends upon an elastic-cord characteristic parameter which exhibits two limiting values corresponding to two nonlinear springs with different Hooke's elastic constants. Additionally, the simplest model of elastic cord dynamics is capable of exhibiting a great diversity of nonlinear phenomena, including bifurcations and chaos, thus providing a suitable alternative model system for discussing the basic essentials of nonlinear dynamics in the context of intermediate physics courses at university level.

A high standard of living causes a large number of irreversible processes, which generate entropy. Energy flow is necessary to remove entropy from the location of generation; commonly this is called energy consumption. The usefulness of an energy flow is defined by its capability of removing entropy from an irreversible process. Fossil energy sources are limited and their use causes ecological damage and conflicts about distribution. As a long-term alternative, energy needs to be obtained from the incoming stream of solar radiation, or indirectly by replacing natural heat engines with artificial ones. Due to the environmental side effects of this replacement, unnecessary artificial entropy production has to be minimized.

The concept of angular jerk is introduced in angular motion in analogy with the linear jerk in translation. The angular jerk vector is defined as the rate of change of the angular acceleration vector, or the third derivative of the angular displacement vector. The existence of angular jerk is demonstrated in Keplerian motion as an example. The angular velocity, angular acceleration and angular jerk vectors are calculated from the polar equation of the orbit and the conservation of angular momentum in terms of the constants of motion. The variations of the angular quantities as functions of the polar angle are studied. Whereas the angular velocity necessarily remains posigrade, the angular acceleration has both posigrade and retrograde phases, and the angular jerk exhibits two posigrade and one retrograde phases during the course of one revolution. The locations of the extrema of the three angular quantities are determined. This treatment is suitable for upper undergraduate physics majors.

Two positively charged pith balls hang from a nail at the end of equal-length strings in Earth's surface gravitational field. The problem consists in finding each of the hanging angles when the balls do not necessarily have the same mass or charge. The solution is an excellent exercise in developing two skills: wisely choosing the coordinate axes in a free-body diagram, and correctly interpreting the roots and limits of a numerical solution. The treatment is accessible to undergraduate physics majors in their first or second year of physics courses.

A short demonstration that the potentials in the Coulomb gauge yield the retarded electric and magnetic fields is presented. This demonstration is relatively simple and can be presented in an advanced undergraduate course of electromagnetic theory.

We discuss, in a pedagogical way, how to solve for relativistic wavefunctions from the radial Dirac equations. We first solve the equations for a linear Lorentz scalar potential, V_s(r), that provides for confinement of a quark; the case of massless u and d quarks is necessarily relativistic. We use an iterative 'shooting and matching' procedure to find the eigenenergies and the upper and lower component wavefunctions. Solutions for the massive quarks (s, c, and b) are also presented. We then consider the Coulomb potential [V_v(r), 0]. We re-derive, numerically, the (analytically well-known) relativistic hydrogen atom eigenenergies and wavefunctions, and later extend that to the cases of heavier one-electron atoms and muonic atoms. Finally, we solve for a combination of the V_s and V_v potentials, when both potentials are linearly confining and V_v has a color Coulombic component. We establish when these potentials give a vanishing spin–orbit interaction (as is approximately the case in quark models of the baryonic spectrum).

The experimental analysis of three-dimensional (3D) movement is of great importance to introduce students to knowledge of the actual physical world. However, the difficulties of collecting 3D data make it little suitable for beginner physics students. In this work, we propose an experiment to analyse 3D motion in stationary and rotating systems. A projectile is launched from a rotating platform. The tracking of the projectile is carried out with the assistance of a stereoscopic camera and simplified object tracking techniques. The experiment can be modelled through the well-known transformation equations between an inertial reference system and a non-inertial one with constant angular velocity. The simplicity of the method and the agreement between the experimental data and the theoretical model make the experiment accessible to undergraduate physics students. In this way, they can easily measure a 3D movement and verify its theoretical equations.

This paper enlarges an undergraduate student project in non-holonomic mechanics (Janová et al 2009 Eur. J. Phys.30 1257–69) by considering rolling friction. In the original problem of coupled rolling motion, the agreement of theory and experiment was demonstrated for the initial part of motion with rolling friction being neglected. As expected, the reality is that rolling friction plays a decisive role during the whole experiment. Extending the correspondence of the model to reality by considering rolling friction, in this paper it is demonstrated that the model satisfactorily explains not only the initial part but also the whole period of the motion observed. Together with the original problem, this paper is an interesting demonstration of the influence of rolling friction and its physical modelling for undergraduate physics education. It also demonstrates that a relatively simple theoretical background can be used for describing realistic situations in mechanics and for explaining experimental results. Moreover, this paper itself can be used by physics teachers as an interesting project in theoretical mechanics that may be solved both separately from and as a follow-up project to Janová et al (2009).

A reason to take ℏ to be positive is presented.