58 research outputs found
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
A derivation of Maxwell’s equations using the Heaviside notation
Maxwell's four differential equations describing electromagnetism are among the most famous equations in science. Feynman said that they provide four of the seven fundamental laws of classical physics. In this paper, we derive Maxwell's equations using a well-established approach for deriving time-dependent differential equations from static laws. The derivation uses the standard Heaviside notation. It assumes conservation of charge and that Coulomb's law of electrostatics and Ampere's law of magnetostatics are both correct as a function of time when they are limited to describing a local system. It is analogous to deriving the differential equation of motion for sound, assuming conservation of mass, Newton's second law of motion and that Hooke's static law of elasticity holds for a system in local equilibrium. This work demonstrates that it is the conservation of charge that couples time-varying E-fields and B-fields and that Faraday's Law can be derived without any relativistic assumptions about Lorentz invariance. It also widens the choice of axioms, or starting points, for understanding 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
Induction and Amplification of Non-Newtonian Gravitational Fields
One obtains a Maxwell-like structure of gravitation by applying the
weak-field approximation to the well accepted theory of general relativity or
by extending Newton's laws to time-dependent systems. This splits gravity in
two parts, namely a gravitoelectric and gravitomagnetic (or cogravitational)
one. Due to the obtained similar structure between gravitation and
electromagnetism, one can express one field by the other one using a coupling
constant depending on the mass to charge ratio of the field source.
Calculations of induced gravitational fields using state-of-the-art fusion
plasmas reach only accelerator threshold values for laboratory testing.
Possible amplification mechanisms are mentioned in the literature and need to
be explored. The possibility of using the principle of equivalence in the weak
field approximation to induce non-Newtonian gravitational fields and the
influence of electric charge on the free fall of bodies are also investigated,
leading to some additional experimental recommendations
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
- …