European Journal of Physics

In 2010, the International Young Physicists' Tournament (IYPT) was introduced to China as an exploratory practical physics activity for young students. Over the past decade, accompanied by annual competitions, students have gradually come to appreciate this research and learning approach around open-ended problems. Since 2018, we have established a lab focused on inquiry-based learning around the annual IYPT problems and redesigned introductory physics laboratory course, serving a large number of first-year students. Since then, the teaching team has continuously refined the teaching process and arrangements. This article focuses on introducing the entire teaching program and student feedback for the redesigned introductory physics laboratory that incorporating IYPT Problems with inquiry-based physics experimental teaching methods to serve a large number of students. We hope to provide valuable references for other institutions.

Nother's theorem is a cornerstone of analytical mechanics, making the link between symmetries and conserved quantities. In this article, I propose a simple, geometric derivation of this theorem that circumvents the usual difficulties that a student of this field usually encounters. The derivation is based on the integration of the differential form dS = pdq − Hdt, where S is the action function, p is the momentum, and H the Hamiltonian, over a closed path.

A non-returning boomerang can fly straight for over one hundred meters, but only if torques with a horizontal component are eliminated by careful shaping of the airfoil. An actuator disk model predicts that non-returning boomerangs must have a negative lift coefficient at both ends, in marked contrast to the returning boomerangs. Stability conditions are examined. The analysis of these ancient hunting weapons is, for the physics student, an instructive exercise in rotational dynamics.

The problem of atomic ionization by the sudden absorption of momentum by its nucleus is studied. By means of a simple one dimensional model we obtain analytical expressions for the re-capture and ionization probabilities. Simple integral formulas for the evaluation of the time evolution of the electronic state are given. Analytical expressions for the ionization probabilities show structures found in realistic three dimensional collisional problems, such as capture probability (by the recoil nucleus) and the binary ionization peak.

Because the relativistic transformation of time involves spatial coordinates, multipole moments can take on very different values in relatively-moving inertial frames. As a related aspect, an infinite solenoid of finite cross-section will have non-zero time-varying electric fields outside its winding arising from the discrete charges carrying the solenoid currents. In the rest frame of the solenoid, the time averages of these time variations vanish and may be ignored. However, these time-varying electric fields have non-zero time averages in an inertial frame where the solenoid is moving perpendicular to its axis, and this non-zero time average plays an important role in the classical electromagnetic interpretation of the Aharonov–Bohm phase shift, which was treated in earlier work. Here we illustrate these ideas for a circular current loop, and then note their applicability to solenoids and toroids. The 'ideal magnetic moment' with no charges and no spatial extent is completely unphysical, and is seen to lead, in a moving inertial frame, to a different and incorrect average electric field from that where discrete charges are used and the radius of the magnetic moment is finite.

It is universally believed that with his 1905 paper 'Does the inertia of a body depend on its energy content?' Einstein first demonstrated the equivalence of mass and energy by making use of his special theory of relativity. In the final step of that paper, however, Einstein equates the kinetic energy of a body to its Newtonian value, indicating that his result is at best a low-velocity approximation. Today, several characters debate whether a mid-nineteenth century physicist, employing only physics available at the time, could plausibly arrive at the celebrated result. In other words, is Einsteinian relativity necessary to derive ${ \mathcal E }={{mc}}^{2}$?

Although synchronization effects play an important role in many areas of basic and applied science, their treatment in undergraduate physics courses requires more attention. Based on acoustic experiments with a driven organ pipe, the article proposes analytical, numerical and qualitative approaches to this universal phenomenon, suitable for introductory teaching. The Adler equation is developed, a first-order nonlinear differential equation describing the phase dynamics of driven self-sustained oscillations in the weak coupling limit. Analytical solutions, intuitive mechanical analogues and properties of the resulting comb spectra are discussed. The underlying phase model is paradigmatic for synchronization-based self-organization phenomena in a wide range of fields, from physics and engineering to life and social sciences.

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 published between 1st January 2012 and 1st January 2023. We evaluated how AR has been used for facilitating learning about physics. Potential AR-based learning activities for different physics topics have been summarized and opportunities, as well as challenges associated with AR-based learning of physics have been reported. It has been shown that AR technologies may facilitate physics learning by providing complementary visualizations, optimizing cognitive load, allowing for haptic learning, reducing task completion time and promoting collaborative inquiry. The potential disadvantages of using AR in physics teaching are mainly related to the shortcomings of software and hardware technologies (e.g. camera freeze, visualization delay) and extraneous cognitive load (e.g. paying more attention to secondary details than to constructing target knowledge).

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 language use in physics are important goals for research on physics learning and instructional design. Qualitative physics education research offers a variety of insights into the characteristics of language and language use in physics such as the differences between everyday language and scientific language, or metaphors used to convey concepts. However, qualitative language analysis fails to capture distributional (i.e. quantitative) aspects of language use and is resource-intensive to apply in practice. Integrating quantitative and qualitative language analysis in physics education research might be enhanced by recently advanced artificial intelligence-based technologies such as large language models, as these models were found to be capable to systematically process and analyse language data. Large language models offer new potentials in some language-related tasks in physics education research and instruction, yet they are constrained in various ways. In this scoping review, we seek to demonstrate the multifaceted nature of language and language use in physics and answer the question what potentials and limitations artificial intelligence-based methods such as large language models can have in physics education research and instruction on language and language use.

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.

How far can we see with the naked eye at night? Many celestial objects like stars and galaxies as well as transient phenomena such as comets and supernovae can be observed in the night sky. We discuss the farthest distances of such objects and phenomena observable with the unaided eye during the night time for Earth bound observers. The physics of night time visual ranges differs from the one of daytime observations because human vision shifts from cones to rods. In addition, mostly point sources are observed, due to the involved large distances. Whether celestial objects and phenomena can be detected depends on the contrast of their radiation and the background sky luminance. We present a concise overview of how far we can see at night by first discussing effects of the earth atmosphere. This includes attenuation of transmitted radiation as well as its role as source of background radiation. Disregarding attenuation of light due to interstellar and intergalactic dust, simple maximum nighttime visual range estimates are based on the inverse square law, which can be easily verified by laboratory and demonstration experiment . From the respective calculations, we find that individual stars within the Milky Way galaxy of up to 15 000 light years are observable. Even farther away are observable galaxies with several billion stars. The Andromeda galaxy can be observed with the naked eye in a distance of around 2.5 million light years. Similarly, the observability of supernovae also allow a visual range beyond the Milky Way galaxy. Finally, gamma ray bursts as the most energetic events in the universe are discussed with regard to naked eye observations.

The theory of the relativistic Doppler effect is well established and validated by several experiments. Most derivations, however, assume that both the reference frame of the source and the reference frame of the receiver are inertial, and the validity of the obtained formulas in the case of a non-inertial source and/or receiver is usually not clarified in higher physics education. As shown in this paper, if such formulas are carelessly applied to non-inertial cases, they can lead to contradictory results. This is probably what happened historically in the interpretation of experiments with a receiver in uniform circular motion around an inertial source, where some authors reported a shift towards the red, some others a shift towards the blue. This confusion points out the importance of establishing Doppler effect formulas that are valid in non-inertial cases. In this paper, we first set a rigorous definition of the relativistic Doppler shift, clarifying that it is the ratio between two proper time intervals relating to two different pairs of events. We then apply the definition to derive the relativistic Doppler shift in the case of a non-inertial source and/or receiver. The proposed derivations are very simple, provide important insights on the correct application of the time dilatation formula to accelerated systems, and highlight possible subtle mistakes that can lead to completely wrong results. This makes them a useful tool for teaching purposes, especially for graduate students.

This work originated as a project in experimental physics conducted by students in the Laboratory of Mechanics and Thermodynamics, a course designed for first-year Physics bachelors. The students were tasked with studying the motion of rigid bodies while having only been introduced to the laws of point-mass dynamics in their theoretical classes. In the proposed experiment, students discovered that bodies with circular symmetry and identical shapes take the same time to roll down an inclined plane. By appropriately fitting the experimental data, they observed that the expression for travel time is equivalent to that of a point mass, except for a multiplicative factor unique to each category of objects. This factor depends on the body's geometry and is directly related to its moment of inertia. Furthermore, we discuss how a similar result can be derived using scaling analysis, illustrating the power of this tool for students early in their physics education. This work may serve as an effective introduction for first-year Physics students to the moment of inertia, as it naturally emerges from a classic physics experiment: the inclined plane.

A new multifunctional apparatus was developed to generate various magnetic fields using a single coil loop, two coil loops (i.e., Helmholtz coil), three coil loops, and a long straight solenoid. The magnetic field formulas were derived based on the Biot-Savart law and the principle of superposition of magnetic fields. The experimental results achieved good agreement with the theoretical predictions, with an error of less than 10.0%。 This compact experimental apparatus is suitable for both theoretical and experimental teaching in college physics.

An undergraduate physics experiment is described that uses a Fabry-Perot etalon and digital camera to determine the hyperfine frequency shifts in naturally occurring mercury. Radiation at 546 nm emitted from the 7 3S1 state relaxing to the 6 3P2 state in a low pressure Hg lamp is selected by an interference filter to pass through the etalon. This produces a series of concentric rings at the focus of the camera lens that are analyzed using bespoke software written for this experiment. Results from the analysis are compared to theoretical calculations of the hyperfine shifts for both the 199Hg and 201Hg isotopes.

The theory of the relativistic Doppler effect is well established and validated by several experiments. Most derivations, however, assume that both the reference frame of the source and the reference frame of the receiver are inertial, and the validity of the obtained formulas in the case of a non-inertial source and/or receiver is usually not clarified in higher physics education. As shown in this paper, if such formulas are carelessly applied to non-inertial cases, they can lead to contradictory results. This is probably what happened historically in the interpretation of experiments with a receiver in uniform circular motion around an inertial source, where some authors reported a shift towards the red, some others a shift towards the blue. This confusion points out the importance of establishing Doppler effect formulas that are valid in non-inertial cases. In this paper, we first set a rigorous definition of the relativistic Doppler shift, clarifying that it is the ratio between two proper time intervals relating to two different pairs of events. We then apply the definition to derive the relativistic Doppler shift in the case of a non-inertial source and/or receiver. The proposed derivations are very simple, provide important insights on the correct application of the time dilatation formula to accelerated systems, and highlight possible subtle mistakes that can lead to completely wrong results. This makes them a useful tool for teaching purposes, especially for graduate students.

This work originated as a project in experimental physics conducted by students in the Laboratory of Mechanics and Thermodynamics, a course designed for first-year Physics bachelors. The students were tasked with studying the motion of rigid bodies while having only been introduced to the laws of point-mass dynamics in their theoretical classes. In the proposed experiment, students discovered that bodies with circular symmetry and identical shapes take the same time to roll down an inclined plane. By appropriately fitting the experimental data, they observed that the expression for travel time is equivalent to that of a point mass, except for a multiplicative factor unique to each category of objects. This factor depends on the body's geometry and is directly related to its moment of inertia. Furthermore, we discuss how a similar result can be derived using scaling analysis, illustrating the power of this tool for students early in their physics education. This work may serve as an effective introduction for first-year Physics students to the moment of inertia, as it naturally emerges from a classic physics experiment: the inclined plane.

An undergraduate physics experiment is described that uses a Fabry-Perot etalon and digital camera to determine the hyperfine frequency shifts in naturally occurring mercury. Radiation at 546 nm emitted from the 7 3S1 state relaxing to the 6 3P2 state in a low pressure Hg lamp is selected by an interference filter to pass through the etalon. This produces a series of concentric rings at the focus of the camera lens that are analyzed using bespoke software written for this experiment. Results from the analysis are compared to theoretical calculations of the hyperfine shifts for both the 199Hg and 201Hg isotopes.

Problem-solving in physics and mathematics has been characterised in terms of five phases by Schoenfeld, and these have previously been used to describe also online and blended behaviour. We argue that expanding the use of server logs to make detailed categorisations of student actions can help increase knowledge about how students solve problems. We present a novel approach for analysing server logs that relies on network analysis and principal component analysis. We used the approach to analyse student interactions with an online textbook that features physics problems. We find five 'components of behavioural structure': Complexity, Linear Length, Navigation, Mutuality, and Erraticism. Further, we find that problem-solving sessions can be divided into four overarching groups that differ in their Complexity and further into ten clusters that also differ on the other components. Analysing typical sessions in each cluster, we find ten different behavioural structures which we describe in terms of Schoenfeld's phases. We suggest that further research integrates this approach with other methodological approaches to get a fuller picture of how learning strategies are used by students in settings with online features.

A simple analytic model for climate and climate change suitable for physics education in upper secondary and tertiary education is presented. It falls into the class of zero-dimensional energy balance models, comprises five independent variables and uses mathematical techniques only at a moderate level. It allows for the definition and discussion of key concepts of climate science such as radiative forcing, climate sensitivity and feedback factors, including an elementary feedback analysis for the four most important fast climate feedbacks. To round off the text, it is briefly shown how the model can be coupled to the ocean as a heat reservoir, providing a rough estimate for the characteristic time scales of climate change. The analysis is formulated rigorously in terms of the model variables.

We revisit the thermodynamic analysis of an isothermal ideal gas mixture enclosed within a cylinder and separated from the surrounding atmosphere by a movable and frictionless piston. When equilibrium conditions based on the chemical potentials of one or more species in the mixture are not satisfied at all times, which occurs for example for a chemical reaction with finite and non-zero reaction rates in the forward and reverse directions and for mass transfer of one species across a permeable membrane occurring at a finite and non-zero rate, an irreversibility is necessarily introduced into the system with a resulting increase in the entropy of the Universe. Consequently, when the piston is set in motion, it cannot oscillate indefinitely. The piston must again come to rest despite there not being any mechanical dissipative mechanisms, i.e. friction or viscous dissipation, nor a thermal dissipative mechanism, i.e. irreversible heat transfer, operating within the system. Only when the system is reversible, such that the entropy of the Universe remains constant at all times, will the piston oscillate indefinitely. 'Chemical damping,' or an irreversibility arising from nonequilibrium conditions on the chemical potential, provides another dissipative mechanism that has not yet been analyzed before.

This article deals with the context of seismology and its relevance to the teaching of physics in a modern and highly motivating way. A modular system called Raspberry Shake RS1D is presented, which is capable of detecting earthquakes as well as everyday vibrations. The Raspberry Shake 1D Vertical Motion Seismograph combines a Raspberry Pi mini-computer, a vertical geophone, a 24-bit digitizer and a near-real-time (miniSEED) data transmission. While the Raspberry Shake is a low cost professional and already well known tool for seismologists, we as physicists 'simply' used that computer-based measurement system. We describe how the seismograph works. We present the detection of ground motion from earthquakes as well as from everyday vibrations using selected examples. Thereby, we focus on teaching physics in the context of seismology, presenting didactic ideas for learning about acoustics, for utilizing measurement systems and for applying scientific methods. This article is especially relevant for teaching undergraduate students. Basic facts about earthquakes that are essential for the study of the seismic phenomena discussed in this article are conveyed.

We explore the matter of Newton's Bucket. To simplify and extend the analysis, we replace the bucket with an infinite cylindrical shell. We show that Newton's mechanical conclusions are equally valid electromagnetically.

The emergence of conversational natural language processing models presents a significant challenge for Higher Education. In this work, we use the entirety of a UK Physics undergraduate (BSc with Honours) degree including all examinations and coursework to test if ChatGPT (GPT-4) can pass a degree. We adopt a 'maximal cheating' approach wherein we permit ourselves to modify questions for clarity, split question up into smaller sub-components, expand on answers given—especially for long form written responses, obtaining references, and use of advanced coaching, plug-ins and custom instructions to optimize outputs. In general, there are only certain parts of the degree in question where GPT-4 fails. Explicitly these include compulsory laboratory elements, and the final project which is assessed by a viva. If these were no issue, then GPT-4 would pass with a grade of an upper second class overall. In general, coding tasks are performed exceptionally well, along with simple single-step solution problems. Multiple step problems and longer prose are generally poorer along with interdisciplinary problems. We strongly suggest that there is now a necessity to urgently re-think and revise assessment practice in physics—and other disciplines—due to the existence of AI such as GPT-4. We recommend close scrutiny of assessment tasks: only invigilated in-person examinations, vivas, laboratory skills testing (or 'performances' in other disciplines), and presentations are not vulnerable to GPT-4, and urge consideration of how AI can be embedded within the disciplinary context.