Comment on `About the magnetic field of a finite wire'

A flaw is pointed out in the justification given by Charitat and Graner [2003 Eur. J. Phys. vol. 24, 267] for the use of the Biot--Savart law in the calculation of the magnetic field due to a straight current-carrying wire of finite length.Comment: REVTeX, 3 pages. A slightly expanded version that has been accepted for publication by Eur. J. Phy

Comment on 'A generalized Helmholtz theorem for time-varying vector fields by A. M. Davis, [Am. J. Phys. 74, 72-76 (2006)]'

In a recent paper Davis formulated a generalized Helmholtz theorem for a time-varying vector field in terms of the Lorenz gauge retarded potentials. The purposes of this comment are to point out that Davis's generalization of the theorem is a version of the extension of the Helmholtz theorem formulated some years ago by McQuistan and also by Jefimenko and more recently by the present author and to show that Davis's expression for the time-dependent vector field is also valid for potentials in gauges other than the Lorenz gau

Poynting Vector Flow in a Circular Circuit

A circuit is considered in the shape of a ring, with a battery of negligible size and a wire of uniform resistance. A linear charge distribution along the wire maintains an electrostatic field and a steady current, which produces a constant magnetic field. Earlier studies of the Poynting vector and the rate of flow of energy considered only idealized geometries in which the Poynting vector was confined to the space within the circuit. But in more realistic cases the Poynting vector is nonzero outside as well as inside the circuit. An expression is obtained for the Poynting vector in terms of products of integrals, which are evaluated numerically to show the energy flow. Limiting expressions are obtained analytically. It is shown that the total power generated by the battery equals the energy flowing into the wire per unit time.Comment: 19 pages, 8 figure

Generalized second-order partial derivatives of 1/r

The generalized second-order partial derivatives of 1/r, where r is the radial distance in 3D, are obtained using a result of the potential theory of classical analysis. Some non-spherical regularization alternatives to the standard spherical-regularization expression for the derivatives are derived. The utility of a spheroidal-regularization expression is illustrated on an example from classical electrodynamics.Comment: 12 pages; as accepted for publication by European Journal of Physic

On the electrodynamics of moving bodies at low velocities

We discuss the seminal article in which Le Bellac and Levy-Leblond have identified two Galilean limits of electromagnetism, and its modern implications. We use their results to point out some confusion in the literature and in the teaching of special relativity and electromagnetism. For instance, it is not widely recognized that there exist two well defined non-relativistic limits, so that researchers and teachers are likely to utilize an incoherent mixture of both. Recent works have shed a new light on the choice of gauge conditions in classical electromagnetism. We retrieve Le Bellac-Levy-Leblond's results by examining orders of magnitudes, and then with a Lorentz-like manifestly covariant approach to Galilean covariance based on a 5-dimensional Minkowski manifold. We emphasize the Riemann-Lorenz approach based on the vector and scalar potentials as opposed to the Heaviside-Hertz formulation in terms of electromagnetic fields. We discuss various applications and experiments, such as in magnetohydrodynamics and electrohydrodynamics, quantum mechanics, superconductivity, continuous media, etc. Much of the current technology where waves are not taken into account, is actually based on Galilean electromagnetism

How to be causal: time, spacetime, and spectra

I explain a simple definition of causality in widespread use, and indicate how it links to the Kramers Kronig relations. The specification of causality in terms of temporal differential eqations then shows us the way to write down dynamical models so that their causal nature /in the sense used here/ should be obvious to all. To extend existing treatments of causality that work only in the frequency domain, I derive a reformulation of the long-standing Kramers Kronig relations applicable not only to just temporal causality, but also to spacetime "light-cone" causality based on signals carried by waves. I also apply this causal reasoning to Maxwell's equations, which is an instructive example since their casual properties are sometimes debated.Comment: v4 - add Appdx A, "discrete" picture (not in EJP); v5 - add Appdx B, cause classification/frames (not in EJP); v7 - unusual model case; v8 add reference

Charges and fields in a current-carrying wire

Charges and fields in a straight, infinite, cylindrical wire carrying a steady current are determined in the rest frames of ions and electrons, starting from the standard assumption that the net charge per unit length is zero in the lattice frame and taking into account a self-induced pinch effect. The analysis presented illustrates the mutual consistency of classical electromagnetism and Special Relativity. Some consequences of the assumption that the net charge per unit length is zero in the electrons frame are also briefly discussed

Axiomatic geometric formulation of electromagnetism with only one axiom: the field equation for the bivector field F with an explanation of the Trouton-Noble experiment

In this paper we present an axiomatic, geometric, formulation of electromagnetism with only one axiom: the field equation for the Faraday bivector field F. This formulation with F field is a self-contained, complete and consistent formulation that dispenses with either electric and magnetic fields or the electromagnetic potentials. All physical quantities are defined without reference frames, the absolute quantities, i.e., they are geometric four dimensional (4D) quantities or, when some basis is introduced, every quantity is represented as a 4D coordinate-based geometric quantity comprising both components and a basis. The new observer independent expressions for the stress-energy vector T(n)(1-vector), the energy density U (scalar), the Poynting vector S and the momentum density g (1-vectors), the angular momentum density M (bivector) and the Lorentz force K (1-vector) are directly derived from the field equation for F. The local conservation laws are also directly derived from that field equation. The 1-vector Lagrangian with the F field as a 4D absolute quantity is presented; the interaction term is written in terms of F and not, as usual, in terms of A. It is shown that this geometric formulation is in a full agreement with the Trouton-Noble experiment.Comment: 32 pages, LaTex, this changed version will be published in Found. Phys. Let

On the gravitodynamics of moving bodies

In the present work we propose a generalization of Newton's gravitational theory from the original works of Heaviside and Sciama, that takes into account both approaches, and accomplishes the same result in a simpler way than the standard cosmological approach. The established formulation describes the local gravitational field related to the observables and effectively implements the Mach's principle in a quantitative form that retakes Dirac's large number hypothesis. As a consequence of the equivalence principle and the application of this formulation to the observable universe, we obtain, as an immediate result, a value of Omega = 2. We construct a dynamic model for a galaxy without dark matter, which fits well with recent observational data, in terms of a variable effective inertial mass that reflects the present dynamic state of the universe and that replicates from first principles, the phenomenology proposed in MOND. The remarkable aspect of these results is the connection of the effect dubbed dark matter with the dark energy field, which makes it possible for us to interpret it as longitudinal gravitational waves.Comment: 18 pages, 4 figures. Final version: almost identical to the reference journal; Cent. Eur. J. Phys. 201