Classical Electromagnetic Interaction of a Charge with a Solenoid or Toroid

IF 1.2 3区 物理与天体物理 Q3 PHYSICS, MULTIDISCIPLINARY
Timothy H. Boyer
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引用次数: 4

Abstract

The Aharonov–Bohm phase shift in a particle interference pattern when electrons pass a long solenoid is identical in form with the optical interference pattern shift when a piece of retarding glass is introduced into one path of a two-beam optical interference pattern. The particle interference-pattern deflection is a relativistic effect of order \(1/c^{2}\), though this relativity aspect is rarely mentioned in the literature. Here we give a thorough analysis of the classical electromagnetic aspects of the interaction between a solenoid or toroid and a charged particle. We point out the magnetic Lorentz force which the solenoid or toroid experiences due to a passing charge. Although analysis in the rest frame of the solenoid or toroid will involve back Faraday fields on the charge, the analysis in the inertial frame in which the charge is initially at rest involves forces due to only electric fields where forces are equal in magnitude and opposite in direction. The classical analysis is made using the Darwin Lagrangian. We point out that the classical analysis suggests an angular deflection independent of Planck’s constant \(\hbar \), where the deflection magnitude is identical with that given by the traditional quantum analysis, but where the deflection direction is unambiguous.

电荷与螺线管或环面的经典电磁相互作用
当电子通过长螺线管时,粒子干涉图样中的Aharonov-Bohm相移在形式上与在双光束干涉图样的一条路径中引入一块缓速玻璃时的光学干涉图样位移相同。粒子干涉图样偏转是阶\(1/c^{2}\)的相对论性效应,尽管这方面的相对论性在文献中很少提及。在这里,我们对电磁线圈或环面与带电粒子之间相互作用的经典电磁方面进行了彻底的分析。我们指出了电磁线圈或环面由于经过的电荷而受到的磁洛伦兹力。虽然在螺线管或环面静止坐标系中的分析将涉及电荷上的反法拉第场,但在电荷最初处于静止状态的惯性坐标系中的分析只涉及由于电场而产生的力,这些力的大小相等,方向相反。经典的分析是用达尔文拉格朗日量进行的。我们指出,经典分析表明角偏转与普朗克常数\(\hbar \)无关,其中偏转幅度与传统量子分析给出的相同,但偏转方向是明确的。
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来源期刊
Foundations of Physics
Foundations of Physics 物理-物理:综合
CiteScore
2.70
自引率
6.70%
发文量
104
审稿时长
6-12 weeks
期刊介绍: The conceptual foundations of physics have been under constant revision from the outset, and remain so today. Discussion of foundational issues has always been a major source of progress in science, on a par with empirical knowledge and mathematics. Examples include the debates on the nature of space and time involving Newton and later Einstein; on the nature of heat and of energy; on irreversibility and probability due to Boltzmann; on the nature of matter and observation measurement during the early days of quantum theory; on the meaning of renormalisation, and many others. Today, insightful reflection on the conceptual structure utilised in our efforts to understand the physical world is of particular value, given the serious unsolved problems that are likely to demand, once again, modifications of the grammar of our scientific description of the physical world. The quantum properties of gravity, the nature of measurement in quantum mechanics, the primary source of irreversibility, the role of information in physics – all these are examples of questions about which science is still confused and whose solution may well demand more than skilled mathematics and new experiments. Foundations of Physics is a privileged forum for discussing such foundational issues, open to physicists, cosmologists, philosophers and mathematicians. It is devoted to the conceptual bases of the fundamental theories of physics and cosmology, to their logical, methodological, and philosophical premises. The journal welcomes papers on issues such as the foundations of special and general relativity, quantum theory, classical and quantum field theory, quantum gravity, unified theories, thermodynamics, statistical mechanics, cosmology, and similar.
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