A. M. Stewart
The instantaneous nature of the potentials of the Coulomb gauge is clarified and a concise derivation is given of the vector potential of the Coulomb gauge expressed in terms of the instantaneous magnetic field.
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The expression for the Coulomb-gauge vector potential in terms of the `instantaneous' magnetic field derived by Stewart [2003 Eur. J. Phys. 24, 519] by employing Jefimenko's equation for the magnetic field and Jackson's formula for the Coulomb-gauge vector potential can be proven much more simply.
The compatibility "demonstrated" by Rovelli & al. between various "gauge conditions" both in Classical Electromagnetism and General Relativity can be better understood if one distinguishes "gauge conditions" of the solution type and "gauge conditions" of the constraint type.
The existence of gauge conditions involving second-order derivatives of potentials is not well known in classical electrodynamics. We introduce one of these gauges, the Coulomb static gauge, in which the scalar potential is given by the Coulomb static potential. We obtain an explicit expression for the associated vector potential and show how the scalar and vector potentials in this gauge yield the retarded electric and magnetic fields. We note the close relation between the proposed gauge and the temporal gauge.
Note on the transformation from the Lorenz gauge to the Coulomb gauge
本文提出了从洛伦兹规范到库仑规范变换的规范函数简单公式，并推导出与Jackson公式等价的替代方程。
A short demonstration that the potentials in the Coulomb gauge yield the retarded electric and magnetic fields is presented. This demonstration is relatively simple and can be presented in an advanced undergraduate curse of electromagnetic theory,
The Coulomb-gauge vector potential of a uniformly moving point charge is obtained by calculating the gauge function for the transformation between the Lorenz and Coulomb gauges. The expression obtained for the difference between the vector potentials in the two gauges is shown to satisfy a Poisson equation to which the inhomogeneous wave equation for this quantity can be reduced. The right-hand side of the Poisson equation involves an important but easily overlooked delta-function term that arises from a second-order partial derivative of the Coulomb potential of a point charge.
It is shown that the well-known procedure for proving the equivalence of the expressions for the electric field calculated using the Lorentz and Coulomb gauges is incorrect. The difference between the two gauges is due to the difference in the speed of propagation of a disturbance of the scalar potential. As an auxiliary result, it is proven that the solution for the electric field cannot be obtained directly from the Maxwell equations, i.e. without introducing the scalar and vector potentials.
In an earlier paper we provided an alternative to the standard gauge concept for deriving the classical electromagnetic wave equations. This alternative involves recognition of two previously overlooked basic equations and represents a simplification of the formalism and a clarification of some basic physics that is obscured in the standard method. It also removes inconsistencies inherent in the gauge approach. The present paper relates to the Coulomb gauge and addresses another example of a major inconsistency that derives directly from the gauge concept
Novel distributional Laplacians and a Coulomb-gauge problem
本文推导 arsinh 函数及相关对数函数的分布拉普拉斯算子，并将其方法用于计算匀速运动点电荷的库仑规范变换函数。
We comment on the work of Tai L Chow, Eur. J. Phys. 18, 467 (1997). By considering the Lagrangians which are uniquely defined only to within an additive total time derivative of a function of co-ordinates and time the author has tried to show that the gauge transformations which relate these Lagrangians are canonical transformations. He has obtained the right conclusion only by using wrong canonical equations and the entire exercise has hence become erroneous and inconclusive. By using the definition of canonical transformation through Poisson brackets we prove that the above gauge transformat…
The main purposes of this paper are (i) to illustrate explicitly by a number of examples the gauge functions chi(x, t) whose spatial and temporal derivatives transform one set of electromagnetic potentials into another equivalent set; and (ii) to show that, whatever propagation or non-propagation characteristics are exhibited by the potentials in a particular gauge, the electric and magnetic fields are always the same and display the experimentally verified properties of causality and propagation at the speed of light. The example of the transformation from the Lorenz gauge (retarded solutions…
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