Table of contents

An experiment and a demonstration concerning transport by magnetic levitation (Maglev) are described. The lift, drag and radial forces on a magnet placed over a rotating conducting disc are measured versus the rotation frequency. The experiment relates to important topics of electromagnetism and could be a useful addition to the undergraduate physics laboratory. The clearly seen electrodynamic suspension is an attractive classroom demonstration.

Exact closed-form solutions of the time-dependent Schrödinger equation are obtained, describing the propagation of wavepackets in the neighbourhood of a potential. Examples given include zero reflection, total reflection and partial reflection of the wavepacket, for the , 1/x² and δ(x) potentials, respectively. In the first two of these cases the results are obtained using the methods of elementary supersymmetric quantum mechanics. This gives an introduction to supersymmetry in its simplest form, suitable for graduate or advanced undergraduate students. Animations of wavepacket propagation are provided.

The quantum efficiency (QE) is an important property of a light detector. This quantity can be determined in the undergraduate physics laboratory. The experimentally determined QE of a silicon photodiode appeared to be in reasonable agreement with expected values. The experiment confirms the quantum properties of light and seems to be a useful addition to other experiments on the photoelectric effect.

We solve for the motion of an object with initial velocity v₀ and subject only to the combined drag of forces linear and quadratic in the velocity. This problem was treated briefly by Newton, after he developed a theoretical argument for the quadratic term, which we now know is characteristic of turbulent flow. Linear drag introduces a time τ, and the two drag forces are equal at a critical velocity v_c; this defines a characteristic distance R = v_cτ; details are discussed for spheres and for cylinders moving along their axis. For v₀/v_c ≫ 1 the role of quadratic drag is largely to reduce the velocity to v_c, below which linear drag dominates. The penetration length is given by L_N = Rln(1 + v₀/v_c). As noted by Gamow, L_N is relevant to the range of non-self-propelled projectiles, such as artillery shells, bullets, ground penetration bombs and spears shot from spearguns; it is also relevant to windmills and fans.

The primary application of dimensional analysis (DA) is in problem solving. Typically, the problem description indicates that a physical quantity Y (the unknown) is a function f of other physical quantities A₁, ..., A_n (the data). We propose a qualitative problem-solving procedure which consists of a parallel decomposition of the original problem into simple special cases. By simple special cases we mean special cases for which, by DA, the unknown function can be completely determined except for a dimensionless multiplicative constant. The concept of significant special representation of the unknown function is introduced.

The Laplace equation has applications in several fields of physics, and problems involving this equation serve as paradigms for boundary value problems. In the case of the Laplace equation in a disc there is a well-known explicit formula for the solution: Poisson's integral. We show how one can derive this formula, and in addition two equivalent but less well-known expressions of a more geometrical character, using little more than elementary geometry.

This paper presents an overview of how circuit models can be used for analysing wave propagation in stratified structures. Relatively complex structures can be analysed using models which are accessible to undergraduate students. Homogeneous slabs are modelled as transmission lines, and thin sheets between the slabs are modelled as lumped elements. It is seen that electric material properties act as shunt elements, and magnetic material properties act as series elements. When the sheets have periodic patterns, they can be represented with resonant circuits. When designing, for instance, an absorber for electromagnetic waves, the circuit models can be used as a starting point to derive a basic, stable design, which can later be optimized using full wave simulations if necessary.

A simple concise relativistic modification of the standard Bohr model for hydrogen-like atoms with circular orbits is presented. As the derivation requires basic knowledge of classical and relativistic mechanics, it can be taught in standard courses in modern physics and introductory quantum mechanics. In addition, it can be shown in a class that one straightforward prediction of this relativistic version of Bohr's model is the impossibility of finding atoms in nature with atomic number larger than a critical value.

This paper revisits the demonstration of Lenz by dropping magnets down a non-magnetic tube. Recent publications are reviewed and ideas for undergraduate laboratory investigations are suggested. Finally, an example of matching theory to observation is presented.

The present state of information communication technology makes it possible to devise and run computer-based e-laboratories accessible to any user with a connection to the Internet, equipped with very simple technical means and making full use of web services. Thus, the way is open for a new strategy of physics education with strongly global features, based on experiment and experimentation. We name this strategy integrated e-learning, and remote experiments across the Internet are the foundation for this strategy. We present both pedagogical and technical reasoning for the remote experiments and outline a simple system based on a server–client approach, and on web services and Java applets. We give here an outline of the prospective remote laboratory system with data transfer using the Internet School Experimental System (ISES) as hardware and ISES WEB Control kit as software. This approach enables the simple construction of remote experiments without building any hardware and virtually no programming, using a paste and copy approach with typical prebuilt blocks such as a camera view, controls, graphs, displays, etc. We have set up and operate at present seven experiments, running round the clock, with more than 12 000 connections since 2005. The experiments are widely used in practical teaching of both university and secondary level physics. The recording of the detailed steps the experimentor takes during the measurement enables detailed study of the psychological aspects of running the experiments. The system is ready for a network of universities to start covering the basic set of physics experiments. In conclusion we summarize the results achieved and experiences of using remote experiments built on the ISES hardware system.

The standard classical mechanics textbooks used at graduate level mention geometrization of the potential motion kinematics. We show that the complete problem can also be geometrized, presenting the system of equations of geometric origin equivalent to the equations of motion of the potential system. The subject seems to be an excellent opportunity for introducing differential geometry concepts already in the classical mechanics course. After presenting the necessary differential geometry notions, the classical mechanical potential system is described in geometric terms. To the system one associates a Riemann space with an appropriately chosen metric and affine connection, both specified by the potential. In this picture, both dynamics and kinematics acquire invariant geometric meaning.

We show that, in their unstable regime of operation, the 'Maxwell–Bloch' equations that describe light–matter interactions inside a bad-cavity-configured laser carry the same resonance properties as any externally driven mechanic or electric oscillator. This finding demonstrates that the nonlinearly coupled laser equations belong to the same universal family of forced oscillatory systems. The primary difference is that while mechanical or electrical systems are put into resonance with an external sinusoidal force with constant amplitude, the resonance curve of the laser equations is described exclusively in terms of linear pump scans, for fixed cavity and material decay rates. In both cases, however, the damping factors play the same fundamental role.

A cheap replica of the verge-and-foliot clock has been built from simple materials. It is a didactic tool of great power for physics teaching at every stage of schooling, in particular at university level. An account is given of its construction and its working principles, together with motivated examples of a few activities.

We present a toy model of quantum electrodynamics (QED) in (1 + 1) dimensions. The QED model is much simpler than QED in (3 + 1) dimensions but exhibits many of the same physical phenomena, and serves as a pedagogical introduction to both QED and quantum field theory in general. We show how the QED model can be derived by quantizing a toy model of classical electrodynamics, and we discuss the connections between the classical and quantum models. In addition, we use the QED model to discuss the radiation of atoms and the Lamb shift.

In this graduate-level theoretical paper, we propose a general derivation of the adiabatic invariant of the n-degree-of-freedom harmonic oscillator, available whichever the physical nature of the oscillator and of the parametrical excitation it undergoes. This derivation is founded on the use of the classical Glauber variables and ends up with this simplest result: the oscillator's adiabatic invariant is just the sum of all the semiclassical quanta numbers associated with its different eigenmodes.

Light beams in wavy unclear water, also called underwater rays, and caustic networks of light formed at the bottom of shallow water are two faces of a single phenomenon. Derivation of the caustic using only simple geometry, Snell's law and simple derivatives accounts for observations such as the existence of the caustic network on vertical walls, the splitting of the networks, the underwater rays and the intensity of a light profile in different depth regimes. As the phenomenon presented is easily observed in nature but rather poorly understood, its explanation may strengthen students' awareness of the connection between physics and everyday life. The explanation of the phenomenon presented is appropriate for undergraduate courses of optics within physics.

In this paper, we show the potential of webcams as precision measuring instruments in a physics laboratory. Various sources of error appearing in 2D coordinate measurements using low-cost commercial webcams are discussed, quantifying their impact on accuracy and precision, and simple procedures to control these sources of error are presented. Finally, an experiment with controlled movement is performed to experimentally measure the errors described above and to assess the effectiveness of the proposed corrective measures. It will be shown that when these aspects are considered, it is possible to obtain errors lower than 0.1%. This level of accuracy demonstrates that webcams should be considered as very precise and accurate measuring instruments at a remarkably low cost.

This contribution adds to the points on the 'indeterminacy of special relativity' made by de Abreu and Guerra. We show that the Lorentz transformation can be composed by the physical observations made in a frame K of events in a frame K', namely (i) objects in K' are moving at a speed v relative to K, (ii) distances and time intervals measured by K' are at variance with those measured by K and (iii) the concept of simultaneity is different in K' compared to K. The order in which the composition is executed determines the nature of the middle aspect (ii). This essential uncertainty of the theory can be resolved only by a universal synchronicity as discussed in [1] based on the unique frame in which the one-way speed of light is constant in all directions.

Geng and Cai suggested a modified He's frequency–amplitude formulation for nonlinear oscillators (Geng and Cai 2007 Eur. J. Phys.28 923–31). We point out the accuracy of both the original one and the modified version depends upon the chosen location point, and so far we have no general rule for the location choice. The method of weighted residuals is suggested to overcome the shortcoming.

We respond to the comment by He (2008 Eur. J. Phys.29 L19) on our work on He's frequency formulation for nonlinear oscillators.

In formulating the Maxwell equations for electrodynamics in the presence of a macroscopic continuous medium, it is common among standard textbooks to simply borrow expressions for the polarization charges and magnetization currents derived in electrostatics and magnetostatics, without much explicit justifications for using them in electrodynamics. Here we emphasize that these quantities must be introduced without resorting to results in statics, and must be derived directly from their definitions which remain valid in the general situation of electrodynamics.