{"title":"Flow of water out of a funnel","authors":"Johann Otto and Carl E Mungan","doi":"10.1088/1361-6404/ad7107","DOIUrl":"https://doi.org/10.1088/1361-6404/ad7107","url":null,"abstract":"The unsteady Bernoulli equation is used to numerically determine the surface height and velocity distribution of water flowing out of a conical tube as a function of time. The speed is found to interpolate between freefall for a cylindrical pipe of constant radius and Torricelli’s law for a funnel having a small exit hole. In addition, the applied force needed to hold the conical vessel in place is calculated using Newton’s second law including the rocket thrust due to the water flowing out of the funnel. A comparison is made with the analogous expressions for the flow through and holding force on a right cylindrical tank having a hole in its bottom face. The level of presentation is appropriate for an undergraduate calculus-based physics course in mechanics that includes a module on fluid dynamics.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183675","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Investigative photometry experiments on planar extended-light sources","authors":"M Campione, A Pietropaolo and G Bussetti","doi":"10.1088/1361-6404/ad6e44","DOIUrl":"https://doi.org/10.1088/1361-6404/ad6e44","url":null,"abstract":"The inverse-square decay law of the illuminance of a point light source with distance is a common notion of basic optics theory, which is readily demonstrated to be a direct consequence of the propagation of spherical wave fronts with the centre at the light source. It is far less common to address the experimental verification of this law and, even less, to study the illuminance decay with the distance of extended light sources, which somehow represent an unknown topic. We propose a scientific experiment where the light sensor of a smartphone is used to collect illuminance data as a function of the source-to-sensor distance and orientation. Through this procedure, students can realize the limit of validity of the inverse-square law and determine the luminance flux of the chosen point-like light source (e.g. the white LED flashlight of a smartphone). More interestingly, when dealing with extended sources (e.g. the LCD of a laptop displaying a white image) subtle characteristics of the decay trend emerge, particularly for distances lower that the source size. A detailed analysis of these characteristics is presented though a process allowing student engagement in a real scientific investigation, envisaging steps of data acquisition through experimental measurements, model construction on the basis of the observed patterns, and finally model testing. We provide a guided formulation for the general modelling of planar emitters, starting from the theoretical treatment of Lambertian sources. In this way, students are able to quantify the luminous emission also for extended sources and their deviation from a Lambertian behaviour.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Drude’s lesser known error of a factor of two and Lorentz’s correction","authors":"Navinder Singh","doi":"10.1088/1361-6404/ad6e46","DOIUrl":"https://doi.org/10.1088/1361-6404/ad6e46","url":null,"abstract":"As is well known, Paul Drude put forward the very first quantitative theory of electrical conduction in metals in 1900. He could successfully account for the Wiedemann–Franz law which states that the ratio of thermal to electrical conductivity divided by temperature is a constant called the Lorenz number. As it turns out, in Drude’s derivation there is a lucky cancellation of two errors. Drude’s underestimatation (by an order of 100) of the value of square of the average electron velocity compensated for his overestimatation of the electronic heat capacity (by the same order of 100). This compensation or cancellation of two errors lead to a value of the Lorenz number very close to its experimental value; which is well known. There is another error of a factor of two which Drude made when he calculated two different relaxation times for heat conductivity and electrical conductivity; in this article we highlight how and why this error occurred in Drude’s derivation and how it was removed 5 years later (in 1905) by Hendrik Lorentz when he used the Boltzmann equation and a single relaxation time. This article is of pedagogical value and may be useful to undergraduate/graduate students learning solid state physics.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183678","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The process of constructing new knowledge: an undergraduate laboratory exercise facilitated by a vacuum capacitor-resistor circuit","authors":"Frank V Kowalski","doi":"10.1088/1361-6404/ad6cb4","DOIUrl":"https://doi.org/10.1088/1361-6404/ad6cb4","url":null,"abstract":"The process of constructing knowledge is typically taught to students by having them reproduce established results (e.g. homework problems). An alternative pedagogical strategy is to illustrate this process using an open problem, such as voltage decay in an <italic toggle=\"yes\">RC</italic> circuit as described below. Analyzing data from this circuit in an undergraduate physics laboratory course reveals a discrepancy between the data and the exponential decay model found in textbooks. As students attempt to reconcile this discrepancy, the instructor can provide guidance in the process of validating data, modeling, and experimental design. This undergraduate laboratory exercise also provides an engaging transition from classroom learning to real world experience.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142227766","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Additional applications of the Lambert W function to solid state physics","authors":"Ahmed Houari","doi":"10.1088/1361-6404/ad6cb3","DOIUrl":"https://doi.org/10.1088/1361-6404/ad6cb3","url":null,"abstract":"Analytical solutions are always desirable in physics for the sake of mathematical exactness and physical insight. In this study, I obtain closed-form analytical expressions for various physical quantities taken from solid state physics. More precisely, I derive analytical expressions in terms of the Lambert W function for the work function and the field-enhancement factor of a field emitting material from the Fowler–Nordheim equation. Additionally, I derive similar analytical expressions for the localization length and the density of states in amorphous semiconductors from the Mott hopping conductivity. Similarly, I also derive analytical formulae based on the Lambert W function to compute the extrinsic-intrinsic transition temperature in a partially compensated semiconductor and the Kondo exchange coupling constant. All the obtained results are exact and explicit. Moreover, some of them allow a direct determination of some physical quantities of interest compared to their indirect determination from semi-logarithmic experimental plots. The findings of this paper are accessible and suitable for students enrolled in graduate solid state physics courses.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183677","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Will Yeadon, Elise Agra, Oto-Obong Inyang, Paul Mackay, Arin Mizouri
{"title":"Evaluating AI and human authorship quality in academic writing through physics essays","authors":"Will Yeadon, Elise Agra, Oto-Obong Inyang, Paul Mackay, Arin Mizouri","doi":"10.1088/1361-6404/ad669d","DOIUrl":"https://doi.org/10.1088/1361-6404/ad669d","url":null,"abstract":"This study aims to compare the academic writing quality and detectability of authorship between human and AI-generated texts by evaluating <italic toggle=\"yes\">n</italic> = 300 short-form physics essay submissions, equally divided between student work submitted before the introduction of ChatGPT and those generated by OpenAI’s GPT-4. In blinded evaluations conducted by five independent markers who were unaware of the origin of the essays, we observed no statistically significant differences in scores between essays authored by humans and those produced by AI (<italic toggle=\"yes\">p</italic>-value = 0.107, <italic toggle=\"yes\">α</italic> = 0.05). Additionally, when the markers subsequently attempted to identify the authorship of the essays on a 4-point Likert scale—from ‘Definitely AI’ to ‘Definitely Human’—their performance was only marginally better than random chance. This outcome not only underscores the convergence of AI and human authorship quality but also highlights the difficulty of discerning AI-generated content solely through human judgment. Furthermore, the effectiveness of five commercially available software tools for identifying essay authorship was evaluated. Among these, ZeroGPT was the most accurate, achieving a 98% accuracy rate and a precision score of 1.0 when its classifications were reduced to binary outcomes. This result is a source of potential optimism for maintaining assessment integrity. Finally, we propose that texts with ≤50% AI-generated content should be considered the upper limit for classification as human-authored, a boundary inclusive of a future with ubiquitous AI assistance whilst also respecting human-authorship.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183679","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ya-Ju Song, Meng-Yao Chai, Xin-Wen Wang, Ji-Bing Yuan, Shi-Qing Tang, Yan Liu
{"title":"Visualization of electromagnetic fields in a circular waveguide using Mathematica","authors":"Ya-Ju Song, Meng-Yao Chai, Xin-Wen Wang, Ji-Bing Yuan, Shi-Qing Tang, Yan Liu","doi":"10.1088/1361-6404/ad6cb5","DOIUrl":"https://doi.org/10.1088/1361-6404/ad6cb5","url":null,"abstract":"This paper employs Mathematica for visualizing electromagnetic fields (EMF) in circular waveguides, effectively addressing pedagogical challenges related to theoretical abstraction and computational complexity. We first derive the exact solutions for guided modes, then summarize the steps for visualizing EMF using Mathematica, propose educational strategies, and showcase simulation results. The Mathematica code is provided, allowing for dynamic parameter adjustment and real-time field change observation. This approach significantly enhances undergraduate students’ understanding of electromagnetism through engaging visual and interactive learning experiences.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183681","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Advanced undergraduate laboratory: exploring isotopic shifts in molecular spectroscopy","authors":"Ye Fei, Yanpeng Ye, Qihang Zhang, Yuzhu Liu","doi":"10.1088/1361-6404/ad6cb2","DOIUrl":"https://doi.org/10.1088/1361-6404/ad6cb2","url":null,"abstract":"Current university physics curricula and pedagogical research lack the study of molecular spectrum and its isotopic effects. In light of this, and considering the simplistic architecture of CN molecules alongside the significance of carbon isotopes in atmospheric cycles and various other disciplines, we have developed an advanced molecular spectroscopy experiment tailored for upper-level undergraduate physics educational courses. Utilizing <sup>12</sup>CO<sub>2</sub> and <sup>13</sup>CO<sub>2</sub> as experimental mediums, this study delves into the exploration of molecular energy level transitions and isotopic effects within molecular spectra through the analysis of CN molecular emission spectra. Additionally, simulations of CN molecular energy level transitions were conducted using LIFBASE software, thereby deepening students’ grasp of molecular energy level quantization. This experiment uses molecular spectrum to realize the interpretation of energy level structure and isotope effects, which is groundbreaking and will add experimental reference and expansion to the teaching of atomic physics.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183680","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Chiral media and optical rotatory dispersion by means of a simple polarimetric experiment for undergraduate students","authors":"Pablo Cortés, Gemma Piquero, J Carlos G de Sande","doi":"10.1088/1361-6404/ad695d","DOIUrl":"https://doi.org/10.1088/1361-6404/ad695d","url":null,"abstract":"A simple experiment taking into account media with natural optical activity and their characterization by means of Mueller polarimetry is proposed for undergraduate Optics and Photonics laboratories. The objectives are, first, to review how to characterize dielectric and homogeneous media with natural optical activity by means of a Mueller matrix, taking into account the variation of these characteristics with wavelength, and combining concepts such as polarimetry, natural optical activity, and rotatory dispersion. Secondly, a complete and simple experiment is proposed to characterize a chiral medium by means of its Mueller matrix for different wavelengths. This experiment can be performed by undergraduate students in a standard optics laboratory. As a particular example of a chiral medium, a quartz crystal is used. The experimental results are compared with those published for crystalline quartz to validate the experiment.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Optical disc structures and diffraction patterns: theoretical foundations and experimental applications","authors":"Yuhang Cheng, Li Zhang, Yaping Zhang","doi":"10.1088/1361-6404/ad6cb0","DOIUrl":"https://doi.org/10.1088/1361-6404/ad6cb0","url":null,"abstract":"This investigation advances the experimental exploration of optical discs’ diffraction phenomena, meticulously constructing optical pathways to ascertain the track pitch within the disc employing both transmission and reflection grating paradigms. Furthermore, this study devises a novel apparatus and methodology for the precise measurement of optical wavelengths, aiming to elucidate the intricate diffraction patterns and the underlying mechanisms of optical discs’ structure. This endeavor not only validates the methodological soundness and efficacy of the proposed approach but also pioneers new avenues for research into physics experiments leveraging optical discs. The application of optical discs in educational settings transcends traditional experimental pedagogy, fostering students’ capabilities to independently conceptualize experiments and delve into scientific explorations.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183768","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}