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Student understanding of the Bloch sphere Eur. J. Phys. (IF 0.7) Pub Date : 2024-02-28 Peter Hu, Yangqiuting Li, Roger S K Mong, Chandralekha Singh
Quantum information science is a rapidly growing interdisciplinary field that is attracting the attention of academics and industry experts alike. It requires talent from a wide variety of traditional fields, including physics, engineering, chemistry, and computer science, to name a few. To prepare students for such opportunities, it is important to give them a strong foundation in the basics of quantum
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Wilks’s theorem, global fits, and neutrino oscillations Eur. J. Phys. (IF 0.7) Pub Date : 2024-02-26 J M Hardin
Tests of models for new physics appearing in neutrino experiments often involve global fits to a quantum mechanical effect called neutrino oscillations. This paper introduces students to methods commonly used in these global fits starting from an understanding of more conventional fitting methods using log-likelihood and χ 2 minimization. Specifically, we discuss how the Δχ 2, which compares the χ
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A simple model for the prediction of CO2 concentrations in the atmosphere, depending on global CO2 emissions Eur. J. Phys. (IF 0.7) Pub Date : 2024-02-23 M Vollmer, W Eberhardt
We present a very simple model for estimating time dependent atmospheric CO2 concentrations c(t) from global carbon emission scenarios, serving as single input data. We derive a single linear differential equation of 1st order, based on parameters which are estimated from quantitative data of the global carbon project and Mauna Loa data for CO2 concentrations. The model is tested first by comparing
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A general derivation of the classical Doppler effect in 3D space Eur. J. Phys. (IF 0.7) Pub Date : 2024-02-21 Francesco Zanchini
The classical Doppler effect has already been studied in many textbooks and papers. However, the formula currently used to describe the Doppler effect for a source and a receiver moving with constant velocities is not suitable for practical applications. Indeed, the formula makes use of two angles that depend on the state of the source-receiver system both at the emission instant and at the reception
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A research-informed graphical tool to visually approach Gauss’ and Stokes’ theorems in vector calculus Eur. J. Phys. (IF 0.7) Pub Date : 2024-02-21 L Hahn, S A Blaue, P Klein
Gauss’ and Stokes’ theorems are fundamental results in vector calculus and important tools in physics and engineering. When students are asked to describe the meaning of Gauss’ divergence theorem, they often use statements like this: ‘The sum of all sources of a vector field in a region gives the net flux out of the region’. In order to raise this description to a mathematically sound level of understanding
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How can the global temperature increase be explained to students? Eur. J. Phys. (IF 0.7) Pub Date : 2024-02-16 R De Luca, V Lamberti
The temperature increase of the system Earth-atmosphere can be described by means of a parallelism between the leaking bucket’s dynamics and the energy balance between the incoming radiant power from the Sun and the outcoming net heat flow rate to outer space. The analogy is interesting from a didactical point of view, since the stable fixed point of the temperature can be related to the height of
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Four errors students make with inverse-square law vectors Eur. J. Phys. (IF 0.7) Pub Date : 2024-02-15 Colin S Wallace, Liam Jones, Alex Lin
In this paper, we discuss four errors introductory physics students make when attempting to add two inverse-square law vectors. We observe multiple instances in which students (1) add vectors as if they were scalars, (2) project the r (or r 2) in the denominator, instead of the entire vector, when attempting to find the vector’s components, (3) incorrectly apply the Pythagorean theorem when attempting
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Can the Dirac deltas in dipole fields be ignored in classical interactions? Eur. J. Phys. (IF 0.7) Pub Date : 2024-02-14 Thales Azevedo
When studying (or teaching) classical electromagnetism, one is bound to deal with the electric field of an ideal electric dipole, as well as its magnetic counterpart. A careful analysis then reveals that each of those fields must include, for consistency, a term proportional to a Dirac delta function localized at the position of the dipole. However, one is usually told not to worry about those terms
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Addendum on ‘Entropy uniqueness determines temperature’ Eur. J. Phys. (IF 0.7) Pub Date : 2024-02-14 Wayne M Saslow
We discuss how to apply the proposed minimum entropy deviation criterion when there is a measurable property P for which there is a statistical mechanical theory as a function of temperature T. When P m can be measured more accurately than heat flow dQ, then P(T) can be inverted to obtain accurate values for T(P); following this, the minimum rms entropy deviation criterion using T(P) then can be used
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A thermoelectric cloud chamber: I. Redesign and operation Eur. J. Phys. (IF 0.7) Pub Date : 2024-02-13 Antoine F Andrade, Lucas W G Souza, Ana P Perini, Lucio P Neves
Developed by CTR Wilson, the cloud chamber was among the most important experimental apparatuses for observing nuclear phenomena in the first half of the twentieth century. Currently, cloud chambers are used as a didactic resource to teach radiation-matter interactions and other Nuclear Physics phenomena. This paper presents the construction of an electrically cooled cloud chamber. This device enables
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A thermoelectric cloud chamber: II. Contributions to medical physics education Eur. J. Phys. (IF 0.7) Pub Date : 2024-02-13 Lucas W G Souza, Ana P Perini, Lucio P Neves
Medical Physics is a branch of science concerned with the application of physical principles in the benefit of health. It is an inherently interdisciplinary field that requires strong skills in various fields of science and technology. Thus, it is challenging for students and their learning processes benefit from teaching methodologies that enable a good understanding of abstract concepts. In this
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Lost work and exergy: two views of the same concept Eur. J. Phys. (IF 0.7) Pub Date : 2024-02-12 Joaquim Anacleto
We present the fundamental equation for a system and for a process, and by considering irreversibility within the system, we show that the lost work concept emerges naturally from the formalism. We then argue that if irreversibility is considered within the surroundings the lost work becomes what is known as exergy. Therefore, lost work and exergy are two views of the same concept, which in turn integrates
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The Coriolis effect and coupled oscillations in a rotating swings amusement ride Eur. J. Phys. (IF 0.7) Pub Date : 2024-02-07 Jurnan P Schilder, Ann-Marie Pendrill
Rotating swings are found in many different versions in parks around the world. They are beautiful examples of the equivalence between gravitational and inertial mass: empty swings and swings with heavy adults hang at the same angle to the vertical. However, sometimes one can notice empty swings moving in a different pattern in an outdoor ride, where wind can induce additional motion, sideways or back
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Does a physical pendulum ever act like a simple pendulum? Eur. J. Phys. (IF 0.7) Pub Date : 2024-02-05 E L Fulton, T J Gay
We show that for a physical pendulum comprising a massive sphere swinging from a massive string, there is, in general, a length of string for which its oscillatory period equals the period calculated by the simple pendulum model with a point-like mass swinging from a massless string whose model length equals the summed length of the real string and the sphere’s radius.
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Physics language and language use in physics—What do we know and how AI might enhance language-related research and instruction Eur. J. Phys. (IF 0.7) Pub Date : 2024-01-29 Peter Wulff
Language is an important resource for physicists and learners of physics to construe physical phenomena and processes, and communicate ideas. Moreover, any physics-related instructional setting is inherently language-bound, and physics literacy is fundamentally related to comprehending and producing both physics-specific and general language. Consequently, characterizing physics language and understanding
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Augmented reality technology in teaching about physics: a systematic review of opportunities and challenges Eur. J. Phys. (IF 0.7) Pub Date : 2024-01-29 Andrej Vidak, Iva Movre Šapić, Vanes Mešić, Vjeran Gomzi
The use of augmented reality (AR) allows for the integration of digital information onto our perception of the physical world. In this article, we present a comprehensive review of previously published literature on the implementation of AR in physics education, at the school and the university level. Our review includes an analysis of 96 papers from the Scopus and Eric databases, all of which were
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How understanding large language models can inform the use of ChatGPT in physics education Eur. J. Phys. (IF 0.7) Pub Date : 2024-01-29 Giulia Polverini, Bor Gregorcic
The paper aims to fulfil three main functions: (1) to serve as an introduction for the physics education community to the functioning of large language models (LLMs), (2) to present a series of illustrative examples demonstrating how prompt-engineering techniques can impact LLMs performance on conceptual physics tasks and (3) to discuss potential implications of the understanding of LLMs and prompt
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Fraunhofer approximation of Fresnel integrals Eur. J. Phys. (IF 0.7) Pub Date : 2024-01-17 K Dupraz, G Dupuis, A Martens, J-M Rax, F Zomer
A method to derive the Fraunhofer diffraction integral by making use of the theory of distributions is presented. With respect to standard textbooks, the pedagogical benefit of this method is that it uniquely uses the far-field approximation of the Fresnel diffraction integral. An operator representation of Fresnel diffraction is also derived.
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A pedagogical approach to introducing the honeycomb lattice gauge theory Eur. J. Phys. (IF 0.7) Pub Date : 2024-01-16 Fei-Jie Huang, Yi-Fen Zhao
A pedagogical approach to introducing the honeycomb lattice gauge theory is presented. Lattice gauge theory, which is an important theory for understanding strongly correlated systems, is a significant topic covered in the quantum field theory course for graduate students. Typically, quantum field theory textbooks introduce lattice gauge theory using the square lattice. However, beginners often find
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Mass formulas for individual black holes in merging binaries Eur. J. Phys. (IF 0.7) Pub Date : 2024-01-16 Zeynep Tugce Ozkarsligil, Bayram Tekin
We give formulas for individual black hole masses in a merger, by using Newtonian physics, in terms of the three measured quantities in the detector: the initial wave frequency f 1, the maximum detected frequency (chirp frequency) f 2, and the time elapse τ between these two frequencies. Newtonian gravity provides an excellent pedagogical tool to understand the basic features of gravitational wave
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Modelling assisted tunneling on the Bloch sphere using the Quantum Composer Eur. J. Phys. (IF 0.7) Pub Date : 2023-12-29 Jonas Bley, Vieri Mattei, Simon Goorney, Jacob Sherson, Stefan Heusler
The Bloch sphere representation is a geometric model for all possible quantum states of a two-level system that can be used to describe the time dynamics of a qubit. As explicit application, we consider the time dynamics of a particle in a double-well potential. In particular, we adopt a recent method for off-resonant excitations, the so-called SUPER principle (Swing Up of the quantum emitter population)
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Berry phase of spin-one system in a rotating electric field Eur. J. Phys. (IF 0.7) Pub Date : 2023-12-29 Abdaljalel Alizzi, Zurab K Silagadze, Artem Uskov
We consider in detail how the Berry phase arises in a rotating electric field in a model system with spin one. The goal is to help the student who first encountered this interesting problem, which is fraught with some subtleties that require attention in order not to go astray.
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An educational model of the Deutsch algorithm for secondary school Eur. J. Phys. (IF 0.7) Pub Date : 2023-12-29 Claudio Sutrini, Giacomo Zuccarini, Massimiliano Malgieri, Maria Bondani, Chiara Macchiavello
In this paper, we present the outline of an educational path to introduce a crucial historical turnpoint of quantum information research—namely the Deutsch algorithm—to secondary school students. We discuss a basic elementarization strategy allowing students to single out and focus on the individual features of quantum mechanics involved in the different steps of the algorithm information processing
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Reply to Comment on ‘Covariant formulation of electrodynamics in isotropic media’ Eur. J. Phys. (IF 0.7) Pub Date : 2023-12-26 Palash B Pal
This note contains my response to the comment written by J Franklin on my paper ‘Covariant formulation of electrodynamics in isotropic media’.
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Should you walk, run or sprint in the rain to get less wet? Eur. J. Phys. (IF 0.7) Pub Date : 2023-12-21 Matteo Zaegel, Mathis Vehils-Vinals, Hugo Guastalla, Benjamin Benabou, Auguste Gires
We have all wondered once whether we should walk, run or sprint in the rain in order to stay as dry as possible. Previous publications already addressed this subject using simple models, as for the shape of the body and the description of the rain and wind. This paper presents a detailed approach which relies on a more realistic ‘human body’ shape and accounts for the variability in time of both the
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Diffraction patterns of optical discs under the far-field condition Eur. J. Phys. (IF 0.7) Pub Date : 2023-12-19 Zhuofan Cai, Shijiang Chen, Boyang Deng, Shuqi Liu, Wei Zhao, Zengming Zhang
When optical discs are illuminated, bright-colored lines can often be observed on the surface of them. Starting from the oblique incident grating diffraction model, this paper analyzes the physical mechanism behind the appearance of these colored lines and provides the coordinate expression of the location of the colored lines on the optical disc under the far-field condition. The wavelength distribution
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The origins of physics words Eur. J. Phys. (IF 0.7) Pub Date : 2023-12-15 P-M Binder
The predominantly Greek and Latin etymological roots that form the core introductory physics vocabulary are identified. They number slightly over 260. Words with other origins and common suffixes are also listed. Definitions are also given for a group of words that have caused difficulties for students in physics classes, contrasting meanings that are, and are not related to physics. A reverse dictionary
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Comment on ‘Covariant formulation of electrodynamics in isotropic media’ Eur. J. Phys. (IF 0.7) Pub Date : 2023-12-13 Jerrold Franklin
A recent paper Pal (2022 Eur. J. Phys. 43 015204) puts into covariant form an extension of relativistic classical electromagnetism from free space to a linearly polarizable medium. The paper is based on the assumption that the relativistic tensor, F μ ν , which is a tensor in free space, will also be a tensor in a linear medium. Pal constructs a proposed covariant formulation that gives Fμν for a
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EMF revisited Eur. J. Phys. (IF 0.7) Pub Date : 2023-12-07 Art Davis
This paper was inspired by a recent publication by Redžíc (2018 Eur. J. Phys. 39 025205) which threw into bold relief the differences between the way Maxwell viewed the current and the way Lorentz visualized it. We make the assumption that for a circuit of laboratory dimensions current (and charge perturbation effects in general) can be assumed to propagate instantaneously around the loop. Our second
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Solving differential equations with deep learning: a beginner’s guide Eur. J. Phys. (IF 0.7) Pub Date : 2023-12-07 Luis Medrano Navarro, Luis Martin-Moreno, Sergio G Rodrigo
The research in artificial intelligence methods with potential applications in science has become an essential task in the scientific community in recent years. Physics-informed neural networks (PINNs) is one of these methods and represents a contemporary technique based on neural network fundamentals to solve differential equations. These networks can potentially improve or complement classical numerical
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Doppler effect in the ripple tank: further experiments with a moving source Eur. J. Phys. (IF 0.7) Pub Date : 2023-12-06 Michele D’Anna, Tommaso Corridoni, Stefano Sposetti, Federico Corni
In this paper, we extend some recent works about the Doppler effect in surface waves on water. We improve the experimental set up by exploring several situations: source in motion with constant velocity and receiver at rest, source at rest and receiver in motion with constant velocity, as well as both source and receiver in motion. Thereby we produce fractional frequency changes Δf/f0 of the order
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The motion of a washer on a vertical steel rod Eur. J. Phys. (IF 0.7) Pub Date : 2023-12-06 Yao Xingxing, Liu Gongyu, Yang Hancheng, Xiao Ting, Zheng Yuan
A washer on a vertical steel rod may start spinning instead of simply sliding down. The forces on the washer are analyzed, and the relationship between the angular velocity of rotation and the angular velocity of precession is obtained. A relationship about the coefficient of friction of the washer is obtained at the condition of rotation without slipping. The influence of the coefficient of friction
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A spherical version of Feynman’s static field momentum example Eur. J. Phys. (IF 0.7) Pub Date : 2023-12-04 Oliver Davis Johns
The Feynman demonstration that electromagnetic field momentum is real—even for static fields—can be made more pedagogically useful by simplifying its geometry. Instead of Feynman’s disk with charged balls on its surface, this article uses the geometry of a hollow non-conducting sphere with uniform surface charge density. With only methods available in a typical upper-division electrodynamics course
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Low-cost measurements of the ‘resonant’ wavelengths reflected by a compact disc under skimming light rays Eur. J. Phys. (IF 0.7) Pub Date : 2023-11-29 M Di Mauro, P Onorato, L M Gratton, R De Luca, O Fiore, L Gislén, A Naddeo
We demonstrate the construction and utilization of an affordable apparatus using readily available materials to accurately measure in a quantitative manner the wavelengths reflected by a compact disc (CD) under skimming light rays. In fact, only a limited number of wavelengths can be revealed when light rays from a white lamp are directed at a CD (or a DVD) in a manner that specifically selects the
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A physical point of view on the arithmetic and geometric mean inequality Eur. J. Phys. (IF 0.7) Pub Date : 2023-11-29 M Modestino, R De Luca, O Faella
We propose a simple experiment designed to justify the arithmetic and geometric mean inequality by means of the laws of thermodynamics. The experiment consists in measuring the entropy variation ΔS in the thermodynamic irreversible process of cooling a metal in water. By considering the metal and water as a single isolated system, the arithmetic and geometric theorem is seen to hold by noticing that
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Hands-on visualization of the effect of fictitious forces with a laser pointer Eur. J. Phys. (IF 0.7) Pub Date : 2023-11-29 Benito Vázquez-Dorrío, Angel Paredes, Miguel Angel Queiruga-Dios
Inertial motion looks like accelerated motion when observed from the point of view of a non-inertial reference frame. A non-inertial observer can then describe the trajectories by introducing fictitious forces, like the centrifugal and Coriolis forces, that arise from the coordinate change between reference frames. This well-known fact is part of the typical Physics syllabus for undergraduate scientists
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Exploring digital signal processing using an interactive Jupyter notebook and smartphone accelerometer data Eur. J. Phys. (IF 0.7) Pub Date : 2023-11-21 P Pirinen, P Klein, S Z Lahme, A Lehtinen, L Rončević, A Susac
Digital signal processing is a valuable practical skill for the contemporary physicist, yet in physics curricula, its central concepts are often introduced either in method courses in a highly abstract and mathematics-oriented manner or in lab work with little explicit attention. In this paper, we present an experimental task in which we focus on a practical implementation of the discrete Fourier transform
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Relativistic mechanics and thermodynamics: IV. Thermodynamic processes Eur. J. Phys. (IF 0.7) Pub Date : 2023-11-21 J Güémez, J A Mier
Two thermodynamic processes, an adiabatic gas compression and an isothermal gas compression, taking place in a moving lab are analysed using a four-vector fundamental equation, dE μ = δ W μ + δ Q μ , a relativistic generalization of the first law of thermodynamics dE = δ W + δ Q. These processes are first described in frame S, with the lab at rest, and then in frame S¯ , moving with constant velocity
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Quantum computing with trapped ions: a beginner’s guide Eur. J. Phys. (IF 0.7) Pub Date : 2023-11-16 Francesco Bernardini, Abhijit Chakraborty, Carlos R Ordóñez
This pedagogical article elucidates the fundamentals of trapped-ion quantum computing, which is one of the potential platforms for constructing a scalable quantum computer. The evaluation of a trapped-ion system’s viability for quantum computing is conducted in accordance with DiVincenzo’s criteria.
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Radioactivity in a bucket Eur. J. Phys. (IF 0.7) Pub Date : 2023-11-16 Luis Peralta
In radiation physics classes, point sources are typically used, for which it is relatively easy to describe the signal obtained by a radiation detector, such as the NaI(Tl) scintillation detector. The use of large extended radiation sources is generally avoided due to the mathematical complexity that their description may involve. However, the use of Monte Carlo simulation methods allows this limitation
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Solving time-independent Schrödinger equation variationally using random numbers Eur. J. Phys. (IF 0.7) Pub Date : 2023-11-15 Pranjal Praneel, Ashish Kumar, Manoj K Harbola
Finding wavefunctions for even the simplest of interacting particle systems consisting of two particles is extremely difficult. It is therefore highly desirable that an accurate and easily implementable method be available to instructors and students of quantum-mechanics for obtaining wavefunctions for these particles. The usual approach taken to do this is to use parametrized functional form for the
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New analytical results in solid state physics using the Lambert W function Eur. J. Phys. (IF 0.7) Pub Date : 2023-11-01 Ahmed Houari
Analytical solutions in physics are always preferred for the sake of mathematical completeness. For this, using the Lambert W function, I derive closed-form analytical expressions for the equilibrium interionic distance in an ionic crystal, the formation energy of a vacancy in a crystal, the zero-temperature energy gap of a clean-limit superconductor and the critical Kosterlitz–Thouless temperature
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Teaching ideal gas in a uniform field: exploring student preferences Eur. J. Phys. (IF 0.7) Pub Date : 2023-11-01 Wittaya Kanchanapusakit, Pattarapon Tanalikhit
An ideal classical gas under uniform gravity is a commonly discussed problem in statistical thermodynamics. At an introductory level, the condition of hydrostatic equilibrium gives rise to the barometric formula, which describes the variation of gas pressure with height. At an advanced level, the partition function can be used to find the density and the internal energy of the gas. These methods rely
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On the connection between Lenz’s law and relativity Eur. J. Phys. (IF 0.7) Pub Date : 2023-10-30 Thales B S F Rodrigues, Bruno F Rizzuti
In this work, we demonstrate explicitly the unified nature of electric and magnetic fields, from the principles of special relativity and Lorentz transformations of the electromagnetic field tensor. Using an operational approach we construct the tensor and its corresponding transformation law, based on the principle of relativity. Our work helps to elucidate concepts of advanced courses on electromagnetism
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A hydraulic energy flow within the moving Earth Eur. J. Phys. (IF 0.7) Pub Date : 2023-10-30 Friedrich Herrmann, Michael Pohlig
We consider the Earth moving through empty space at 30 km s−1 (in the Sun’s frame of reference). Associated with this motion is a convective flow of kinetic and internal energy. Since there is high pressure inside the Earth, and since the Earth is moving, there is yet another ‘hydraulic’ energy flow. This latter is what this article is about. Although this energy flow is huge, it is not addressed in
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Students’ confusions about the electric field of a uniformly moving charge Eur. J. Phys. (IF 0.7) Pub Date : 2023-10-27 Petar Žugec, Davor Horvatić, Ivica Smolić
In light of a recent direct experimental confirmation of a Lorentz contraction of Coulomb field (an electric field of a point charge in a uniform motion), we revisit some common confusions related to it, to be mindful of in teaching the subject. These include questions about the radial nature of the field, the role of the retardation effect due to a finite speed of information transfer and some issues
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From Galilean relativity to special relativity: the pedagogical contribution of the space-proper time diagrams Eur. J. Phys. (IF 0.7) Pub Date : 2023-10-27 Alain Kirèche
After detailing the characteristics of space-proper time diagrams for Galilean relativity and special relativity, we show how they can be used to better visualize the progression of ideas about the absolute or relative nature of space and time, from Galilean relativity to special relativity. We conclude that space-proper time diagrams could be an interesting new tool for introducing special relativity
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An elementary approach to simulating the perihelion of Mercury Eur. J. Phys. (IF 0.7) Pub Date : 2023-10-27 Hollis Williams
The relativistic correction to the precession of the perihelion of Mercury provided key evidence for the accuracy of general relativity as a theory of gravity. This example still has a large amount of potential to introduce students to the power of numerical simulations in theoretical physics, but existing approaches may be too detailed for many students and involve them beginning to learn a programming
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Packing soft spheres: experimental demonstrations with hydrogels Eur. J. Phys. (IF 0.7) Pub Date : 2023-10-25 A Irannezhad, A Baragry, D Weaire, A Mughal, S Hutzler
We describe a number of different experimental set-ups that use hydrogel spheres to demonstrate dense packings of deformable spheres in various geometries. The arrangements are similar to those of bubbles in foams, drops in emulsions, biological cells, etc. The experiments are easy to perform in the class-room or an undergraduate science laboratory. They are described in the context of the history
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Semiclassical calculation of the pendulum period Eur. J. Phys. (IF 0.7) Pub Date : 2023-10-25 Theodosios Geo Douvropoulos
In this paper, we calculate the swing period of the classical pendulum via semiclassical path-integration. We point out the significance of the classical periodic orbits and the equivalence of pendulum’s classical isochronism to the equidistance of the quantum energy levels. We derive the swing period in terms of the semiclassical tunneling time and the fractional revival period. A possible definition
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Study on the magnetic levitation of a magnetic flea Eur. J. Phys. (IF 0.7) Pub Date : 2023-10-19 Yuchen Jiang, Jin Wang, Xiaojie Wang
We investigated the problem of ‘magnetic levitation’ originating from the 33rd International Young Physicists’ Tournament (IYPT). The problem was first investigated by a PRL paper (Baldwin et al.) in 2018, which states that the flea of a magnetic stirrer spinning fast enough in a liquid with a high viscosity coefficient can jump from the bottom and levitate stably. The magnetic force and gravity balance
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Percolation of ‘civilisation’ in a homogeneous isotropic universe Eur. J. Phys. (IF 0.7) Pub Date : 2023-10-17 A L Alinea, C J C Jadrin
In this work, we consider the spread of a ‘civilisation’ in an idealised homogeneous isotropic universe where all the planets of interest are habitable. Following a framework that goes beyond the usual idea of percolation in common undergraduate computational physics textbooks, we investigate the behaviour of the number of colonised planets with time, and the total colonisation time for three types
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(Avoided) crossings in the spectra of matrices with globally degenerate eigenvalues Eur. J. Phys. (IF 0.7) Pub Date : 2023-10-17 S Silliman, M Bhattacharya
(Avoided) crossings are ubiquitous in physics and are connected to many physical phenomena such as hidden symmetries, the Berry phase, entanglement, Landau–Zener processes, the onset of chaos, etc. A pedagogical approach to cataloging (avoided) crossings has been proposed in the past, using matrices whose eigenvalues avoid or cross as a function of some parameter. The approach relies on the mathematical
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Pressure gradient in an incompressible fluid as a reaction force and the preservation of the principle of ‘cause and effect’ Eur. J. Phys. (IF 0.7) Pub Date : 2023-10-17 Lachezar S Simeonov
When considering the motion of an incompressible fluid, it is common practice to take the curl on both sides of the Navier–Stokes (or Euler) equations and cancel the pressure force. The governing equations are sufficient to derive the velocity field of the fluid without any knowledge of the pressure. In fact, the pressure is only calculated after obtaining the velocity field. This raises a number of
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Smooth and oscillatory geometric phase corrections for driven spins Eur. J. Phys. (IF 0.7) Pub Date : 2023-10-10 M V Berry
For a quantum spin driven cyclically by a slowly-rotated magnetic field, geometric phases are well understood. If the cycle takes a long time T, the leading-order (dynamical) phase is proportional to T and the geometric phase is the contribution independent of T. The dynamical and geometric phases are the first two terms of a series in slowness 1/T. Here it is shown with an exactly solvable example
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Visualization of cylindrical resonances Eur. J. Phys. (IF 0.7) Pub Date : 2023-10-09 Brais Vila
The analysis of cylindrical resonators is part of standard physics curricula but, unlike for their rectangular counterpart, their mode structure is hardly ever visualized. The aim of this work is to show a way of doing it, providing a set of interactive web applications and citing potential use cases in the form of both academic courses and published research. These cover several branches of physics
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Challenges in addressing student difficulties with basics and change of basis for two-state quantum systems using a multiple-choice question sequence in online and in-person classes Eur. J. Phys. (IF 0.7) Pub Date : 2023-10-05 Peter Hu, Yangqiuting Li, Chandralekha Singh
Research-validated multiple-choice questions comprise an easy-to-implement instructional tool for scaffolding student learning and providing formative assessment of students’ knowledge. We present findings from the implementation of a research-validated multiple-choice question sequence on the basics of two-state quantum systems, including inner products, outer products, translation between Dirac notation
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The electric flux through a square of a point charge near one corner Eur. J. Phys. (IF 0.7) Pub Date : 2023-10-03 Elisabeth Atems
This paper presents two geometric models that can be used by students studying electrostatics to explore the electric flux of a point charge through a square in the limit of infinitesimal displacement from one corner. We first use qualitative reasoning to show that the limit is not a single value, but depends on the direction of displacement, and has significant discontinuities at the plane inside
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On the ball on a string demonstration of angular momentum conservation Eur. J. Phys. (IF 0.7) Pub Date : 2023-10-03 Andrea Sacchetti
The ‘ball on a string’ demonstration is a common tool used in physics education to illustrate the concept of conservation of angular momentum. However, various confounding factors can cause significant deviations from the idealized case, particularly under extreme conditions or when using low-stiffness pivots or high coefficients of friction. These factors include air resistance, contact friction at
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Measuring capacitor charge and discharge using an LED and a smartphone Eur. J. Phys. (IF 0.7) Pub Date : 2023-09-29 R Hurtado-Gutiérrez, Á Tejero
In this article, we present a simple, inexpensive, and effective method for measuring the capacitor charge and discharge processes using a light-emitting diode (LED) and the light meter of a smartphone. We propose a simple circuit in which the LED’s brightness is linear on the capacitor’s voltage, allowing us to use the smartphone to monitor the capacitor state accurately. The method is tested experimentally