Showing papers on "Scalar potential published in 1967"
TL;DR: In this article, the Laplace force was applied to a moving magnetic charge R and a varying dipole of moment M undergoes a force E × dM dt, and a slowly varying current of intensity i a force ( di dt )∳V O l, where V denotes the scalar potential.
31 citations
TL;DR: In this article, the problem of radiation from sources of arbitrary time dependence in a moving conducting medium is treated, where the medium is assumed to be homogeneous and isotropic, with permittivity e, permeability μ and conductivity σ, and to move with constant velocity v with respect to a given inertial reference frame.
Abstract: This paper treats the problem of radiation from sources of arbitrary time dependence in a moving conducting medium. The medium is assumed to be homogeneous and isotropic, with permittivity e, permeability μ, and conductivity σ, and to move with constant velocity v with respect to a given inertial reference frame. v may have any value up to the speed of light. It is shown how the Maxwell‐Minkowski equations for the electromagnetic fields in the moving medium can be integrated by means of a pair of vector and scalar potential functions analogous to those commonly used with stationary media. The wave equation associated with these potential functions is derived, and an associated scalar Green's function is defined. The solution for the Green's function is obtained in closed form, by means of a technique making use of the relation between the fundamental solution of a radiation problem and that of a corresponding Cauchy initial‐value problem. The resulting Green's function is found to consist of an oblate sph...
20 citations
TL;DR: In this article, a general procedure for axially symmetric magnetostatic field mapping is presented for the case of magnet poles, which is suitable for field mapping when ion or electron optical lenses are dealt with.
6 citations
TL;DR: In this article, a method to evaluate the scalar potential of axially symmetric fields is surveyed and its extent of validity is investigated and the field form in the median plane of round poles is derived at several pole thicknesses and separations.
3 citations
TL;DR: In this paper, necessary and sufficient conditions for separability of the Schrodinger equation with a vector potential were given for the Klein-Gordon case and the physical meaning of the condition on the vector potential was visualized with the aid of gauge invariance.
Abstract: Necessary and sufficient conditions are given for separability of the Schrodinger equation with a vector potential The physical meaning of the condition on the vector potential is visualized with the aid of gauge invariance The analysis can be carried out formally for the Klein-Gordon case
2 citations
TL;DR: In this paper, the covariant Larmor theorem is derived for an inviscid charged fluid in the presence of an arbitrary electromagnetic field and a gravitational field which is described by a simple scalar potential.
Abstract: The covariant Larmor theorem is derived within the framework of special relativity for an inviscid charged fluid in the presence of an arbitrary electromagnetic field and a gravitational field which is described by a simple scalar potential. The flow need not be adiabatic or barotropic. The covariant form of the Larmor theorem, which is an antisymmetric tensor equation, is equivalent to two 3-vector equations, one of which is the equation of motion of the fluid. The other is just the familiar 3-vector statement of the Larmor theorem except for an extra precession that is thermal in origin. The relativistic Helmholtz equation for the fluid vorticity is derived from the covariant Larmor theorem. If the vorticity is defined as the curl of the usual canonical momentum of a charged particle in an electromagnetic field, then it is found that the vorticity flux diffuses through the fluid unless the flow is isentropic. If, however, the vorticity is defined as the curl of a generalized canonical momentum that includes an appropriate thermal 4-potential, then it is found that the flux of this generalized vorticity, called theintrinsic vorticity, remains frozen in the fluid even when viscosity is present and the flow is nonadiabatic. When expressed in terms of the intrinsic vorticity, the generalized Helmholtz equation may be given a simple microscopic interpretation.
TL;DR: In this article, the authors investigated the effect of spherical condensers on the reduced Laplace equation and showed that the problem may be approximately solved by some analytical method relying on the theory of complex functions.