In the last 30 days

• Open/close More on the asymmetric infinite square well: energy eigenstates with zero curvature

  L P Gilbert et al 2005 Eur. J. Phys. 26 815 Tag this article

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  We extend the standard treatment of the asymmetric infinite square well to include solutions that have zero curvature over part of the well. This type of solution, both within the specific context of the asymmetric infinite square well and within the broader context of bound states of arbitrary piecewise-constant potential energy functions, is not often discussed as part of quantum mechanics texts at any level. We begin by outlining the general mathematical condition in one-dimensional time-independent quantum mechanics for a bound-state wavefunction to have zero curvature over an extended region of space and still be a valid wavefunction. We then briefly review the standard asymmetric infinite square well solutions, focusing on zero-curvature solutions as represented by energy eigenstates in position and momentum space.

• Open/close A little help for a better understanding and application of Faraday's law

  E Benedetto et al 2012 Eur. J. Phys. 33 L15 Tag this article

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  In this letter, we examine Faraday's law of induction, analysing the electromotive force generated by a Lorentz force and the one generated by an electric field due to a changing magnetic field. We obtain the result in a didactically simple and appealing way. The final formula is derived considering explicitly the dependence of the magnetic field on the space coordinates, which is often neglected in standard textbooks.

• Open/close Laplace boundary-value problem in paraboloidal coordinates

  L Duggen et al 2012 Eur. J. Phys. 33 689 Tag this article

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  This paper illustrates both a problem in mathematical physics, whereby the method of separation of variables, while applicable, leads to three ordinary differential equations that remain fully coupled via two separation constants and a five-term recurrence relation for series solutions, and an exactly solvable problem in electrostatics, as a boundary-value problem on a paraboloidal surface. In spite of the complex nature of the former, it is shown that the latter solution can be quite simple. Results are provided for the equipotential surfaces and electric field lines are given near a paraboloidal conductor.

• Open/close Reconnections of wave vortex lines

  M V Berry and M R Dennis 2012 Eur. J. Phys. 33 723 Tag this article

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  When wave vortices, that is nodal lines of a complex scalar wavefunction in space, approach transversely, their typical crossing and reconnection is a two-stage process incorporating two well-understood elementary events in which locally coplanar hyperbolas switch branches. The explicit description of this reconnection is a pedagogically useful illustration of several concepts: singularity, codimension, unfolding, genericity, bifurcation and normal forms.

• Open/close Photonic crystals: a unique partnership between light and matter

  R H Lipson and C Lu 2009 Eur. J. Phys. 30 S33 Tag this article

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  Photonic crystals are periodic dielectric structures with an index of refraction periodicity of the order of the wavelength of light. They are emerging as a key building block for many applications in nanotechnology that involve controlling the flow of light. In this paper, the basic physical principles and applications of photonic crystals are presented, as well as descriptions of some of the many chemical and physical strategies that have been used for their fabrication.

• Open/close A laboratory activity on the eddy current brake

  J A Molina-Bolívar and A J Abella-Palacios 2012 Eur. J. Phys. 33 697 Tag this article

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  The aim of this paper is to introduce a simple and low-cost experimental setup that can be used to study the eddy current brake, which considers the motion of a sliding magnet on an inclined conducting plane in terms of basic physical principles. We present a set of quantitative experiments performed to study the influence of the geometrical and electromagnetic properties of the magnet on the magnetic drag force. This video-based experiment is ideal for the study of kinematic graphs and the application of Newton's laws. Video motion analysis software enables students to make precise measurements of the magnet's position at incremental times during its motion, thus allowing them to quantify electromagnetic induction phenomena. The equipment needed for this experiment and data collection software are present in most physics teaching laboratories or are inexpensive and available.

• Open/close Exploring the role of physics representations: an illustrative example from students sharing knowledge about refraction

  Tobias Fredlund et al 2012 Eur. J. Phys. 33 657 Tag this article

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  Research has shown that interactive engagement enhances student learning outcomes. A growing body of research suggests that the representations we use in physics are important in such learning environments. In this paper we draw on a number of sources in the literature to explore the role of representations in interactive engagement in physics. In particular we are interested in the potential for sharing disciplinary knowledge inherent in so-called persistent representations (such as equations, diagrams and graphs), which we use in physics. We use selected extracts from a case study, where a group of senior undergraduate physics students are asked to explain the phenomenon of refraction, to illustrate implications for interactive engagement. In this study the ray diagram that was initially introduced by the students did not appear to sufficiently support their interactive engagement. However, the introduction of a wavefront diagram quickly led their discussion to an agreed conclusion. From our analysis we conclude that in interactive engagement it is important to choose appropriate persistent representations to coordinate the use of other representations such as speech and gestures. Pedagogical implications and future research are proposed.

• Open/close The effects of the Pauli exclusion principle in determining the ionization energies of the helium atom and helium-like ions

  F A Deeney and J P O'Leary 2012 Eur. J. Phys. 33 667 Tag this article

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  For helium and helium-like ions, we have examined the differences between the values of the ionization energies as calculated from the Bohr theory and those measured in experiments. We find that these differences vary linearly with the atomic number of the system. Using this result, we show how the Bohr model for single-electron systems may be modified in a simple way so that it may be applied to two-electron systems as well.

• Open/close Testing plastic deformations of materials in the introductory undergraduate mechanics laboratory

  C M Romo-Kröger 2012 Eur. J. Phys. 33 551 Tag this article

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  Normally, a mechanics laboratory at the undergraduate level includes an experiment to verify compliance with Hooke's law in materials, such as a steel spring and an elastic rubber band. Stress–strain curves are found for these elements. Compression in elastic bands is practically impossible to achieve due to flaccidity. A typical experiment for the complete loading–unloading cycle is to subject a tubular object to torsion. This paper suggests simple experiments for studying properties concerning elasticity and plasticity in elements of common use, subjected to stretching or compression, and also torsion reinforcing. The experiments use plastic binders, rubber bands and metal springs under a moderate load. This paper discusses an experiment with an original device to measure torsion deformations as a function of applied torques, which permitted construction of the hysteresis cycle for a rubber hose and various tubes. Another experiment was designed to define the temporal recovery of a plastic spring with initial stretching. A simple mathematical model was developed to explain this phenomenon.

• Open/close Chemical potential for the interacting classical gas and the ideal quantum gas obeying a generalized exclusion principle

  F J Sevilla and L Olivares-Quiroz 2012 Eur. J. Phys. 33 709 Tag this article

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  In this work, we address the concept of the chemical potential μ in classical and quantum gases towards the calculation of the equation of state μ = μ( n, T) where n is the particle density and T the absolute temperature using the methods of equilibrium statistical mechanics. Two cases seldom discussed in elementary textbooks are presented with detailed calculations. The first one refers to the explicit calculation of μ for the interacting classical gas exemplified by van der Waals gas. For this purpose, we used the method described by van Kampen (1961 Physica 27 783). The second one refers to the calculation of μ for ideal quantum gases that obey a generalized Pauli's exclusion principle that leads to statistics that go beyond the Bose–Einstein and Fermi–Dirac cases. The audience targeted in this work corresponds mainly to advanced undergraduates and graduate students in the physical–chemical sciences but it is not restricted to them. In regard of this, we have put a special emphasis on showing some additional details of calculations that usually do not appear explicitly in textbooks.