{"title":"Four errors students make with inverse-square law vectors","authors":"Colin S Wallace, Liam Jones, Alex Lin","doi":"10.1088/1361-6404/ad2391","DOIUrl":"https://doi.org/10.1088/1361-6404/ad2391","url":null,"abstract":"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 <italic toggle=\"yes\">r</italic> (or <italic toggle=\"yes\">r</italic>\u0000<sup>2</sup>) in the denominator, instead of the entire vector, when attempting to find the vector’s components, (3) incorrectly apply the Pythagorean theorem when attempting to calculate the magnitude of the resultant vector, and (4) incorrectly relate the signs of the components of an electric field (or force) to the signs of the electric charges. While these are not the only errors students make, they are the most frequently occurring based on our analysis of 678 exams taken by students in either introductory mechanics or electricity and magnetism (E&M). We then show how these errors can be encoded into a new type of activity or assessment question which we call a ‘student error task.’ Introductory physics instructors can use the student error task in this paper as a way to engage or assess their students’ understandings of how to add two inverse-square law vectors.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"68 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140007989","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":"Can the Dirac deltas in dipole fields be ignored in classical interactions?","authors":"Thales Azevedo","doi":"10.1088/1361-6404/ad2392","DOIUrl":"https://doi.org/10.1088/1361-6404/ad2392","url":null,"abstract":"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 since, as classical interactions always involve sources which are spatially separated, the Dirac-delta terms are only relevant for quantum mechanics, where they are directly related to important phenomena. In this work, we pose and solve a purely classical problem in electrostatics in which the Dirac-delta terms in the dipole fields are indispensable. It involves the computation of the interaction energy between a conductor with a spherical cavity and an (ideal) electric dipole located at the center of that cavity. We also solve its magnetic counterpart, replacing the conductor with a superconductor and the electric dipole with a magnetic one.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"24 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140011479","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":"Lost work and exergy: two views of the same concept","authors":"Joaquim Anacleto","doi":"10.1088/1361-6404/ad2101","DOIUrl":"https://doi.org/10.1088/1361-6404/ad2101","url":null,"abstract":"We present the fundamental equation for a system and for a process, and by considering irreversibility within the system, we show that the <italic toggle=\"yes\">lost work</italic> 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 <italic toggle=\"yes\">exergy</italic>. Therefore, lost work and exergy are two views of the same concept, which in turn integrates a broader and more fundamental concept: <italic toggle=\"yes\">entropy generation</italic>. It is our opinion that the clarification of the meanings of lost work and exergy, as well as the discussion that leads to an understanding of their differences and similarities, has not received the attention in the literature that it deserves. This paper fills that gap, and it is hoped that the discussion of these two concepts here will be useful for both students and teachers.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"13 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139754131","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":"Mass formulas for individual black holes in merging binaries","authors":"Zeynep Tugce Ozkarsligil, Bayram Tekin","doi":"10.1088/1361-6404/ad1531","DOIUrl":"https://doi.org/10.1088/1361-6404/ad1531","url":null,"abstract":"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 <italic toggle=\"yes\">f</italic>\u0000<sub>1</sub>, the maximum detected frequency (chirp frequency) <italic toggle=\"yes\">f</italic>\u0000<sub>2</sub>, and the time elapse <italic toggle=\"yes\">τ</italic> between these two frequencies. Newtonian gravity provides an excellent pedagogical tool to understand the basic features of gravitational wave observations, but it must be augmented with the assumption of gravitational radiation from General Relativity for accelerating masses as there is no gravitational wave Newtonian gravity. The simplest approach would be to consider a binary system of two non-spinning masses (two black holes) circling their common center of mass. All the computations can be done within Newtonian physics, but the General Relativistic formula for the power carried by gravitational waves is required in this scheme. It turns out there is a subtle point: for the consistency of this simple, yet pedagogical computation, taking the lowest order power formula from General Relativity leads to complex individual masses. Here we remedy this problem and suggest a way to write down an average power formula coming from perturbative General Relativity.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"20 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139509867","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":"Berry phase of spin-one system in a rotating electric field","authors":"Abdaljalel Alizzi, Zurab K Silagadze, Artem Uskov","doi":"10.1088/1361-6404/ad1398","DOIUrl":"https://doi.org/10.1088/1361-6404/ad1398","url":null,"abstract":"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.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"27 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139095539","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}
Jonas Bley, Vieri Mattei, Simon Goorney, Jacob Sherson, Stefan Heusler
{"title":"Modelling assisted tunneling on the Bloch sphere using the Quantum Composer","authors":"Jonas Bley, Vieri Mattei, Simon Goorney, Jacob Sherson, Stefan Heusler","doi":"10.1088/1361-6404/ad139a","DOIUrl":"https://doi.org/10.1088/1361-6404/ad139a","url":null,"abstract":"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) driven by periodic electromagnetic fields, to the context of quantum tunnelling. We show that the tunnelling probability can be enhanced significantly when an appropriate oscillation of the potential height is introduced. Driven by a collaborative approach we call <italic toggle=\"yes\">educator-developer dialogue</italic>, an updated version of the software Quantum Composer is presented. For educational purposes, we map the two lowest energy states of the 1D-Schrödinger equation to the Bloch sphere representation, leading to a rather clear and intuitive physical picture for the pertinent time dynamics.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"30 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139096195","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":"Reply to Comment on ‘Covariant formulation of electrodynamics in isotropic media’","authors":"Palash B Pal","doi":"10.1088/1361-6404/ad0dea","DOIUrl":"https://doi.org/10.1088/1361-6404/ad0dea","url":null,"abstract":"This note contains my response to the comment written by J Franklin on my paper ‘Covariant formulation of electrodynamics in isotropic media’.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"205 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139054611","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 origins of physics words","authors":"P-M Binder","doi":"10.1088/1361-6404/ad0f9b","DOIUrl":"https://doi.org/10.1088/1361-6404/ad0f9b","url":null,"abstract":"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 of roots, showing the individual origin of about 400 words in all areas of introductory physics is presented in an appendix. The information presented here can inform and assist in developing a physics lexicon in minority and indigenous languages and to create classroom moments that connect the origin of words with everyday life.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"34 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138685252","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":"Comment on ‘Covariant formulation of electrodynamics in isotropic media’","authors":"Jerrold Franklin","doi":"10.1088/1361-6404/ad0de9","DOIUrl":"https://doi.org/10.1088/1361-6404/ad0de9","url":null,"abstract":"A recent paper Pal (2022 <italic toggle=\"yes\">Eur. J. Phys.</italic>\u0000<bold>43</bold> 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, <italic toggle=\"yes\">F</italic>\u0000<sup>\u0000<italic toggle=\"yes\">μ</italic>\u0000<italic toggle=\"yes\">ν</italic>\u0000</sup>, which is a tensor in free space, will also be a tensor in a linear medium. Pal constructs a proposed covariant formulation that gives <inline-formula>\u0000<tex-math>\u0000<?CDATA ${F}^{mu nu }$?>\u0000</tex-math>\u0000<mml:math overflow=\"scroll\"><mml:msup><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>μ</mml:mi><mml:mi>ν</mml:mi></mml:mrow></mml:msup></mml:math>\u0000<inline-graphic xlink:href=\"ejpad0de9ieqn1.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula> for a medium moving with constant velocity, <bold>v</bold>, in terms of <italic toggle=\"yes\">F</italic>\u0000<sup>\u0000<italic toggle=\"yes\">μ</italic>\u0000<italic toggle=\"yes\">ν</italic>\u0000</sup> for the medium at rest. However, although <italic toggle=\"yes\">F</italic>\u0000<sup>\u0000<italic toggle=\"yes\">μ</italic>\u0000<italic toggle=\"yes\">ν</italic>\u0000</sup> has been proven to be a relativistic tensor in free space, we show that it is not a tensor in a linear medium. This means that the covariant extension proposed by Pal fails.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"11 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138685133","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}
K. Dupraz, Guillaume Dupuis, A. Martens, J. Rax, F. Zomer
{"title":"Fraunhofer approximation of Fresnel integrals","authors":"K. Dupraz, Guillaume Dupuis, A. Martens, J. Rax, F. Zomer","doi":"10.1088/1361-6404/ad1530","DOIUrl":"https://doi.org/10.1088/1361-6404/ad1530","url":null,"abstract":"\u0000 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.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"105 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139004554","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}