Pub Date : 2023-10-25DOI: 10.1088/1361-6404/ad06bf
Matteo Zaegel, Mathis Vehils-Vinals, Hugo Guastalla, Benjamin Benabou, Auguste Gires
Abstract We have all wondered once whether we should walk, run or sprint under 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 of the variability in time of both the wind and the rain drop size and velocity distributions. It appears that in some seldom cases with tailwind and light rain, there is an optimum velocity, but in general it is better to run as fast as possible. While 'running' instead of 'walking' yields significant gain, the extra effort required to 'sprint' is not always worth it.
{"title":"Should you walk, run or sprint in the rain to get less wet?","authors":"Matteo Zaegel, Mathis Vehils-Vinals, Hugo Guastalla, Benjamin Benabou, Auguste Gires","doi":"10.1088/1361-6404/ad06bf","DOIUrl":"https://doi.org/10.1088/1361-6404/ad06bf","url":null,"abstract":"Abstract We have all wondered once whether we should walk, run or sprint under 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 of the variability in time of both the wind and the rain drop size and velocity distributions. It appears that in some seldom cases with tailwind and light rain, there is an optimum velocity, but in general it is better to run as fast as possible. While 'running' instead of 'walking' yields significant gain, the extra effort required to 'sprint' is not always worth it.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134973479","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}
Pub Date : 2023-10-25DOI: 10.1088/1361-6404/ad06be
Francesco Bernardini, Abhijit Chakraborty, Carlos R Ordonez
Abstract 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.
{"title":"Quantum computing with trapped ions: a beginner's guide","authors":"Francesco Bernardini, Abhijit Chakraborty, Carlos R Ordonez","doi":"10.1088/1361-6404/ad06be","DOIUrl":"https://doi.org/10.1088/1361-6404/ad06be","url":null,"abstract":"Abstract 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.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134973345","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}
Pub Date : 2023-10-19DOI: 10.1088/1361-6404/acfd23
Yuchen Jiang, Jin Wang, Xiaojie Wang
Abstract 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 periodically. This phenomenon includes several concepts: magnetic dipoles, rigid-body rotation, fluid mechanics and magnetic levitation. They are more or less unfamiliar to undergraduate students. However, the movement of the flea could be described with a concise forced vibration equation, which is familiar in textbooks. The phenomenon could be divided into two stages: synchronous movement and levitation state. The transition is the jumping of the flea. We demonstrated this process and presented several equations to build this physical model. The progression of the phenomenon is due to the increase in the drive magnet angular velocity called the drive velocity. We verified our theory by simulation and experiments. Several parameters are experimentally verified to influence the phenomenon. We also discussed the origin of dynamic stabilization, which would be slightly complicated but worthy for students. In short, we introduce an interesting problem originating from the PRL paper that can be easily achieved under laboratory conditions. We extend some content in a pedagogical way that would be helpful for students to understand the related physical concepts, such as the influence of the viscosity coefficient of the liquid on the flea’s motion, which is not discussed in the PRL paper.
摘要:我们研究了起源于第33届国际青年物理学家锦标赛(IYPT)的“磁悬浮”问题。2018年，PRL的一篇论文(Baldwin et al.)首先研究了这个问题，该论文指出，磁性搅拌器的跳蚤在高粘度系数的液体中旋转得足够快，可以从底部跳起并稳定悬浮。磁力和重力周期性地平衡。这种现象包括几个概念:磁偶极子、刚体旋转、流体力学和磁悬浮。对于本科生来说，它们或多或少有些陌生。然而，跳蚤的运动可以用一个简明的强迫振动方程来描述，这在教科书中是熟悉的。这种现象可分为两个阶段:同步运动和悬浮状态。过渡是跳蚤的跳跃。我们演示了这个过程，并提出了几个方程来建立这个物理模型。这种现象的进展是由于驱动磁体角速度的增加，称为驱动速度。我们通过仿真和实验验证了我们的理论。实验验证了几个参数对这一现象的影响。我们还讨论了动态稳定的起源，这可能有点复杂，但值得学生学习。简而言之，我们引入了一个有趣的问题，起源于PRL论文，可以很容易地在实验室条件下实现。我们以教学的方式扩展了一些有助于学生理解相关物理概念的内容，例如液体粘度系数对跳蚤运动的影响，这在PRL论文中没有讨论。
{"title":"Study on the Magnetic Levitation of a Magnetic Flea","authors":"Yuchen Jiang, Jin Wang, Xiaojie Wang","doi":"10.1088/1361-6404/acfd23","DOIUrl":"https://doi.org/10.1088/1361-6404/acfd23","url":null,"abstract":"Abstract We investigated the problem of ‘magnetic levitation’ originating from the <?CDATA $33mathrm{rd}$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mn>33</mml:mn> <mml:mi>rd</mml:mi> </mml:math> 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 periodically. This phenomenon includes several concepts: magnetic dipoles, rigid-body rotation, fluid mechanics and magnetic levitation. They are more or less unfamiliar to undergraduate students. However, the movement of the flea could be described with a concise forced vibration equation, which is familiar in textbooks. The phenomenon could be divided into two stages: synchronous movement and levitation state. The transition is the jumping of the flea. We demonstrated this process and presented several equations to build this physical model. The progression of the phenomenon is due to the increase in the drive magnet angular velocity called the drive velocity. We verified our theory by simulation and experiments. Several parameters are experimentally verified to influence the phenomenon. We also discussed the origin of dynamic stabilization, which would be slightly complicated but worthy for students. In short, we introduce an interesting problem originating from the PRL paper that can be easily achieved under laboratory conditions. We extend some content in a pedagogical way that would be helpful for students to understand the related physical concepts, such as the influence of the viscosity coefficient of the liquid on the flea’s motion, which is not discussed in the PRL paper.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135667264","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}
Pub Date : 2023-10-17DOI: 10.1088/1361-6404/acfdd9
Lachezar Slavchev Simeonov
Abstract 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 conceptual problems. For instance, why is the pressure unnecessary for obtaining the velocity field? Traditionally, forces have been considered as the ‘causes’ of motion, and the resulting acceleration as the ‘effect’. However, the acceleration (the effect) and the resulting velocity field can be obtained without any recourse to the pressure (the cause), seemingly violating the principle of ‘cause’ and ‘effect’. We address these questions by deriving the pressure force of an incompressible fluid, starting from d’Alembert’s principle of virtual work, as a ‘reaction force’ that maintains the incompressibility condition. Next, we show that taking the curl on both sides of the Navier–Stokes (or Euler) equations is equivalent to using d’Alembert’s principle of virtual work, which cancels out the virtual work of the pressure gradient. This shows that abstract procedures, such as taking the curl on both sides of an equation, can actually be tacit applications of rich physical principles, without one realizing it. This can be quite instructive in a classroom of undergraduate students.
{"title":"Pressure Gradient in an Incompressible Fluid as a Reaction Force and the Preservation of the Principle of `Cause and Effect`","authors":"Lachezar Slavchev Simeonov","doi":"10.1088/1361-6404/acfdd9","DOIUrl":"https://doi.org/10.1088/1361-6404/acfdd9","url":null,"abstract":"Abstract 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 conceptual problems. For instance, why is the pressure unnecessary for obtaining the velocity field? Traditionally, forces have been considered as the ‘causes’ of motion, and the resulting acceleration as the ‘effect’. However, the acceleration (the effect) and the resulting velocity field can be obtained without any recourse to the pressure (the cause), seemingly violating the principle of ‘cause’ and ‘effect’. We address these questions by deriving the pressure force of an incompressible fluid, starting from d’Alembert’s principle of virtual work, as a ‘reaction force’ that maintains the incompressibility condition. Next, we show that taking the curl on both sides of the Navier–Stokes (or Euler) equations is equivalent to using d’Alembert’s principle of virtual work, which cancels out the virtual work of the pressure gradient. This shows that abstract procedures, such as taking the curl on both sides of an equation, can actually be tacit applications of rich physical principles, without one realizing it. This can be quite instructive in a classroom of undergraduate students.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135945122","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}
Pub Date : 2023-10-17DOI: 10.1088/1361-6404/acfbc5
Allan Lambit Alinea, Cedrix Jadrin
Abstract 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 of universes. These include static, dark energy-dominated, and matter-dominated universes. For all these types of universes, we find a remarkable fit with the Logistic Growth Function for the number of colonised planets with time. This is in spite of the fact that for the matter- and dark-energy dominated universes, the space itself is expanding. For the total colonisation time, T , the case for a dark energy-dominated universe is marked with divergence beyond the linear regime characterised by small values of the Hubble parameter, H . Not all planets in a spherical section of this universe can be ‘colonised’ due to the presence of a shrinking Hubble sphere. In other words, the recession speeds of other planets go beyond the speed of light making them impossible to reach. On the other hand, for a matter-dominated universe, while there is an apparent horizon, the Hubble sphere is growing instead of shrinking. This leads to a finite total colonisation time that depends on the Hubble parameter characterising the Universe; in particular, we find T ∼ H for small H and T ∼ H 2 for large H .
{"title":"Percolation of 'Civilisation' in a Homogeneous Isotropic Universe","authors":"Allan Lambit Alinea, Cedrix Jadrin","doi":"10.1088/1361-6404/acfbc5","DOIUrl":"https://doi.org/10.1088/1361-6404/acfbc5","url":null,"abstract":"Abstract 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 of universes. These include static, dark energy-dominated, and matter-dominated universes. For all these types of universes, we find a remarkable fit with the Logistic Growth Function for the number of colonised planets with time. This is in spite of the fact that for the matter- and dark-energy dominated universes, the space itself is expanding. For the total colonisation time, T , the case for a dark energy-dominated universe is marked with divergence beyond the linear regime characterised by small values of the Hubble parameter, H . Not all planets in a spherical section of this universe can be ‘colonised’ due to the presence of a shrinking Hubble sphere. In other words, the recession speeds of other planets go beyond the speed of light making them impossible to reach. On the other hand, for a matter-dominated universe, while there is an apparent horizon, the Hubble sphere is growing instead of shrinking. This leads to a finite total colonisation time that depends on the Hubble parameter characterising the Universe; in particular, we find T ∼ H for small H and T ∼ H 2 for large H .","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135944288","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}
Pub Date : 2023-10-17DOI: 10.1088/1361-6404/acfbc4
Sam Silliman, Mishkatul Bhattacharya
Abstract (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 tool of the discriminant, which can be calculated from the characteristic polynomial of the matrix, and whose roots as a function of the parameter being varied yield the locations as well as degeneracies of the (avoided) crossings. In this article we consider matrices whose symmetries force two or more eigenvalues to be degenerate across the entire range of variation of the parameter of interest, thus leading to an identically vanishing discriminant. To show how this case can be handled systematically, we introduce a perturbation to the matrix and calculate the roots of the discriminant in the limit as the perturbation vanishes. We show that this approach correctly generates a nonzero ‘reduced’ discriminant that yields the locations and degeneracies of the (avoided) crossings. We illustrate our technique using the matrix Hamiltonian for benzene in Hückel theory, which has recently been discussed in the context of (avoided) crossings in its spectrum.
{"title":"(Avoided) crossings in the spectra of matrices with globally degenerate eigenvalues","authors":"Sam Silliman, Mishkatul Bhattacharya","doi":"10.1088/1361-6404/acfbc4","DOIUrl":"https://doi.org/10.1088/1361-6404/acfbc4","url":null,"abstract":"Abstract (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 tool of the discriminant, which can be calculated from the characteristic polynomial of the matrix, and whose roots as a function of the parameter being varied yield the locations as well as degeneracies of the (avoided) crossings. In this article we consider matrices whose symmetries force two or more eigenvalues to be degenerate across the entire range of variation of the parameter of interest, thus leading to an identically vanishing discriminant. To show how this case can be handled systematically, we introduce a perturbation to the matrix and calculate the roots of the discriminant in the limit as the perturbation vanishes. We show that this approach correctly generates a nonzero ‘reduced’ discriminant that yields the locations and degeneracies of the (avoided) crossings. We illustrate our technique using the matrix Hamiltonian for benzene in Hückel theory, which has recently been discussed in the context of (avoided) crossings in its spectrum.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135944289","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}
Pub Date : 2023-10-13DOI: 10.1088/1361-6404/ad0346
Luis Peralta
Abstract 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 to be overcome. Potassium chloride, containing the 40K isotope, is an ideal candidate for carrying out this type of experiment. The source activity is obtained through the detection of the 1460.8 keV gamma- photon emitted in the 40K decay. In the first experiment, a cylindrical container is used, placing the NaI(Tl) detector in its center and filling the remaining space with potassium chloride. In a second, more complex case, a large radioactive source consisting of a container filled with a mixture of sand and potassium chloride, with the NaI(Tl) detector placed in the center of the mixture, is used. In this case, the mass of potassium chloride is approximately 1/5 of the sand mass. In both experiments, the detection efficiency is obtained by Monte Carlo simulation. A careful analysis of the experimental data allows to obtain a good agreement between the measured and calculated value of the activity.
{"title":"Radioactivity in a bucket","authors":"Luis Peralta","doi":"10.1088/1361-6404/ad0346","DOIUrl":"https://doi.org/10.1088/1361-6404/ad0346","url":null,"abstract":"Abstract 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 to be overcome. Potassium chloride, containing the 40K isotope, is an ideal candidate for carrying out this type of experiment. The source activity is obtained through the detection of the 1460.8 keV gamma- photon emitted in the 40K decay. In the first experiment, a cylindrical container is used, placing the NaI(Tl) detector in its center and filling the remaining space with potassium chloride. In a second, more complex case, a large radioactive source consisting of a container filled with a mixture of sand and potassium chloride, with the NaI(Tl) detector placed in the center of the mixture, is used. In this case, the mass of potassium chloride is approximately 1/5 of the sand mass. In both experiments, the detection efficiency is obtained by Monte Carlo simulation. A careful analysis of the experimental data allows to obtain a good agreement between the measured and calculated value of the activity.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135853737","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}
Pub Date : 2023-10-11DOI: 10.1088/1361-6404/ad026a
Friedrich Herrmann, Michael Pohlig
Abstract We consider the Earth moving through empty space at 30 km/s (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 the textbooks. The reason is that for the explanation one needs a concept which is not introduced in traditional presentations of classical gravitation: the gravitomagnetic field. The corresponding theory, gravitoelectromagnetism, was formulated in 1893 by Heaviside in analogy to Maxwell's theory of electromagnetism.

We discuss the question of what are the sources and sinks of this hydraulic, non-convective energy flow. To answer the question, we need to study the energy flow density distribution within the gravitational field. In doing so, we will make some interesting observations. The energy flow within the field is twice as large as it should be to transfer the field energy from one side of the Earth to the other. The excess flow goes back through the matter of the Earth.

Since our readers may not be familiar with Heaviside’s theory, we first treat the electromagnetic analogue of our problem and then translate the results to the gravitational situation.
{"title":"A hydraulic energy flow within the moving Earth","authors":"Friedrich Herrmann, Michael Pohlig","doi":"10.1088/1361-6404/ad026a","DOIUrl":"https://doi.org/10.1088/1361-6404/ad026a","url":null,"abstract":"Abstract We consider the Earth moving through empty space at 30 km/s (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 the textbooks. The reason is that for the explanation one needs a concept which is not introduced in traditional presentations of classical gravitation: the gravitomagnetic field. The corresponding theory, gravitoelectromagnetism, was formulated in 1893 by Heaviside in analogy to Maxwell's theory of electromagnetism.&#xD;&#xD;We discuss the question of what are the sources and sinks of this hydraulic, non-convective energy flow. To answer the question, we need to study the energy flow density distribution within the gravitational field. In doing so, we will make some interesting observations. The energy flow within the field is twice as large as it should be to transfer the field energy from one side of the Earth to the other. The excess flow goes back through the matter of the Earth.&#xD;&#xD;Since our readers may not be familiar with Heaviside’s theory, we first treat the electromagnetic analogue of our problem and then translate the results to the gravitational situation.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136063101","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}
Pub Date : 2023-10-11DOI: 10.1088/1361-6404/ad026b
J Güémez, Jose Angel Mier
Abstract 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, ${rm d} E^mu = delta W^mu + delta Q^mu$, a relativistic generalization of the first law of thermodynamics ${rm d}E=delta W+ delta Q$. These processes are first described in frame S, with the lab at rest, and then in frame ${bar {rm S}}$, moving with constant velocity relative to S. This formalism shows that Lorentz transformation preserves the principle of relativity in thermodynamics. The physical meaning of the norm of a four-vector is analysed, and Clausius definition of entropy variation is generalised to relativity. The classical description of the process is obtained in a moving lab by taking the low-speed limit in the four-vector fundamental equation. The formalism naturally incorporates the role of the laws of mechanics when analysing processes that are typically considered as purely thermodynamic.
{"title":"Relativistic Mechanics and Thermodynamics. IV. Thermodynamic processes","authors":"J Güémez, Jose Angel Mier","doi":"10.1088/1361-6404/ad026b","DOIUrl":"https://doi.org/10.1088/1361-6404/ad026b","url":null,"abstract":"Abstract 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, ${rm d} E^mu = delta W^mu + delta Q^mu$, a relativistic generalization of the first law of thermodynamics ${rm d}E=delta W+ delta Q$. These processes are first described in frame S, with the lab at rest, and then in frame ${bar {rm S}}$, moving with constant velocity relative to S. This formalism shows that Lorentz transformation preserves the principle of relativity in thermodynamics. The physical meaning of the norm of a four-vector is analysed, and Clausius definition of entropy variation is generalised to relativity. The classical description of the process is obtained in a moving lab by taking the low-speed limit in the four-vector fundamental equation. The formalism naturally incorporates the role of the laws of mechanics when analysing processes that are typically considered as purely thermodynamic.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136063376","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}
Pub Date : 2023-10-09DOI: 10.1088/1361-6404/ad0187
Petar Zugec, Horvatic Davor, Ivica Smolić
Abstract 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 the questions about a radial nature of the field, a role of the retardation effect due to a finite speed of information transfer and some issues related to a depiction of Coulomb field by means of the Lorentz contracted field lines.
{"title":"Students' confusions about the electric field of a uniformly moving charge","authors":"Petar Zugec, Horvatic Davor, Ivica Smolić","doi":"10.1088/1361-6404/ad0187","DOIUrl":"https://doi.org/10.1088/1361-6404/ad0187","url":null,"abstract":"Abstract 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 the questions about a radial nature of the field, a role of the retardation effect due to a finite speed of information transfer and some issues related to a depiction of Coulomb field by means of the Lorentz contracted field lines.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135044464","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：