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首页> 外文期刊>Journal of Physics, A. Mathematical and General: A Europhysics Journal >Darwin-Lagrangian analysis for the interaction of a point charge and a magnet: considerations related to the controversy regarding the Aharonov-Bohm and Aharonov-Casher phase shifts
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Darwin-Lagrangian analysis for the interaction of a point charge and a magnet: considerations related to the controversy regarding the Aharonov-Bohm and Aharonov-Casher phase shifts

机译：关于点电荷与磁体相互作用的达尔文-拉格朗日分析：与有关阿哈罗诺夫-波姆和阿哈罗诺夫-卡希尔相移的争论有关的考虑因素

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摘要

The classical electromagnetic interaction of a point charge and a magnet is discussed by first calculating the interaction of a point charge with a simple model magnetic moment and then suggesting a multiparticle limit. The Darwin-Lagrangian is used to analyse the electromagnetic behaviour of the model magnetic moment (composed of two oppositely charged particles of different masses in an initially circular Coulomb orbit) interacting with a passing point charge. Considerations of force, energy, momentum and Centre of energy are treated through second order in 1/c. The changing magnetic moment is found to put a force back on a passing charge; this force is of order 1/c(2) and depends upon the magnitude of the magnetic moment. The limit of a many-particle magnet at-ranged as a toroid is discussed. It is suggested that in the multiparticle limit, the electric fields of the passing charge are screened out of the body of the magnet while the magnetic fields of the passing charge penetrate into the body of the magnet. This is consistent with our understanding of the penetration of electromagnetic velocity fields into ohmic conductors. The proposed multiparticle limit is consistent with the conservation laws for energy and momentum, as well as constant motion of the Centre of energy, and Newton's third law for the net Lorentz forces on the magnet and on the point charge. The work corresponds to a classical electromagnetic analysis of the interaction which is basic to understanding the controversy over the Aharonov-Bohm and Aharonov-Casher phase shifts and represents a refutation of the suggestions of Aharonov, Pearle and Vaidman.
机译：通过首先计算具有简单模型磁矩的点电荷的相互作用，然后提出多粒子极限，来讨论点电荷与磁体的经典电磁相互作用。达尔文-拉格朗日算子用于分析模型磁矩（由初始圆形库仑轨道中质量不同的两个带相反电荷的粒子组成）与通过点电荷相互作用的电磁行为。力，能量，动量和能量中心的考虑通过1 / c中的二阶处理。发现变化的磁矩将力加回到通过的电荷上。该力约为1 / c（2），并取决于磁矩的大小。讨论了多粒子磁体在环形范围内的极限。建议在多粒子极限中，将通过电荷的电场从磁体的主体中屏蔽掉，而使通过电荷的磁场渗透到磁体的主体中。这与我们对电磁速度场渗透到欧姆导体中的理解是一致的。拟议的多粒子极限与能量和动量的守恒定律，能量中心的恒定运动以及磁体和点电荷上的净洛伦兹力的牛顿第三定律相一致。这项工作对应于相互作用的经典电磁分析，这对于理解关于Aharonov-Bohm和Aharonov-Casher相移的争论是基本的，并且代表了对Aharonov，Pearle和Vaidman的建议的驳斥。

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