Showing papers on "Magnetic potential published in 1978"

Derivation of Maxwell’s equations from the local gauge invariance of quantum mechanics

Abstract: Maxwell’s equations are derived from the principle of form invariance of quantum mechanics under multiplication of the wave function by a space‐ and time‐dependent phase factor (local gauge transformations of the first kind). The principle leads to the introduction of the vector and scalar potentials, which are shown to transform under the usual gauge transformations of electromagnetism (gauge transformations of the second kind). The electric and magnetic fields are introduced in the usual way to obtain observable fields which are gauge independent. Faraday’s law and the condition of no magnetic monopoles are obtained from the gauge transformations of the potentials. Conservation of energy and the linearity of the field equations are assumed to obtain Gauss’ law and the Ampere‐Maxwell law.

Derivation of the quasi-linear equation in a magnetic field

Abstract: A formal derivation of the quasi-linear equation of a plasma in a magnetic field is presented. The theory accounts for spatial inhomogeneity in one direction and for bounce motion of particles confined in a mirror magnetic field.

The Zero-Range Potential Model and Its Application in Atomic and Molecular Physics

Abstract: Publisher Summary This chapter discusses the zero-range potential model (ZRPM) and its application in atomic and molecular physics. The ZRPM is a method of treating the problem of a particle in the field of a short-range potential well when there is a shallow energy level near the boundary of the continuum spectrum. The basic idea of ZRPM is to replace the Schrodinger equation inside the well by a certain boundary condition on the wavefunction at the center of the well. The ZRPM can be easily generalized for the case when there are several potential wells at rest or moving and also when, besides the wells, there are electric and magnetic fields. The chapter also discusses the basic relations and presents some applications of one- and many-center boundary conditions in atomic and molecular physics. A charged particle was studied under the action of (1) a homogeneous electric field, (2) a homogeneous magnetic field, (3) crossed electric and magnetic fields, (4) a rotating electric field, and (5) a Coulomb field of a point charge.

Induction in arbitrarily shaped oceans—III. Oceans of finite conductivity

Abstract: Summary. Approximate methods of solution for induction in arbitrarily shaped oceans, derived earlier for ‘oceans of infinite conductivity, are extended to cover cases where the oceans are of finite conductivity. The method enables the magnetic potential to be evaluated without undue effort. It is further shown how these ideas link up with integro-differential formulations involving either the oceanic electric current density or its associated current function. The problem of uniqueness of solution when there are two or more land masses is finally considered.

Magnetostatic modes of stripe domain structure

Abstract: In connection with our study of ferromagnetic resonance in nonsaturated magnetic films or platelets, we have also considered the spectrum of magnetostatic modes for a stripe domain structure. For materials with large q (=HA/4πMs), the domain walls are very thin compared to the stripe width and the effective internal field, including anisotropy and demagnetizing fields, is relatively uniform within each domain. In a film of finite thickness the modes are essentially those given by Damon and van de Vaart for a disk uniformly magnetied normal to the plane. Only volume waves are permitted. If there is a nonzero component of the propagation vector in the direction of the intersection of the film plane and the domain wall, the magnetic potential must vanish at each wall. This condition requires that the propagation constant associated with the direction normal to the walls=integer×π/domain width. The domain walls are ’’transparent’’ for propagation normal to their planes and the corresponding magnetostatic mode...

Comparisons of measured and calculated potential magnetic fields.

Abstract: Photospheric line-of-sight and transverse magnetic field data obtained with the Marshall Space Flight Center vector magnetograph system for an isolated sunspot are described A study of the linear polarization patterns and of the calculated transverse field lines indicates that the magnetic field of the region is very nearly potential The Hα fibril structures of this region as seen in high resolution photographs corroborate this conclusion Consequently, a potential field calculation is described using the measured line-of-sight fields together with assumed Neumann boundary conditions; both are necessary and sufficient for a unique solution The computed transverse fields are then compared with the measured transverse fields to verify the potential field model and assumed boundary values The implications of these comparisons on the validity of magnetic field extrapolations using potential theory are discussed

A heuristic potential theory of electric and magnetic monopoles without strings

Abstract: A simple spherical distribution of electric and/or magnetic charge moves with a constant velocity with respect to an observer in the laboratory frame. The electric and magnetic potentials are written in the rest frame of the two types of charge, and in the laboratory frame by means of the Lorentz transformation. The E and H fields are evaluated and are shown to be consistent with Maxwell’s equations, generalized to include magnetic charge. In this development a ’’scalar’’ rather than a ’’vector’’ potential is used to describe the magnetic monopole at rest, thus avoiding ’’string theory.’’ This approach leads to a more complicated, but still useful form for the classical Lagrangian.

Synthesis of inductive displacement-measuring system using computer-aided design

Abstract: A rigorous method used to model linear variable differential transformers (l.v.d.t.s) is applied to a variable-inductance displacement transducer. This method known as `field modelling? uses a knowledge of the magnetic flux distribution within the transducer. This flux distribution is obtained from the solution of Maxwell's equation, with boundary conditions deriving from the geometry and material properties of the transducer. The field equations are expressed in terms of the magnetic vector potential and, with the use of axial symmetry, reduced to an elliptic boundary value problem. This problem is approximated by finite-difference equations and solved, numerically, by the method of successive overrelaxation (s.o.r.). A transducer design is modelled, using this method, and the model is used in the synthesis of a displacement-measuring system. The sensitivity of the synthesised system is compared with experimental results obtained from a system with the same design specifications. The sensitivities of the two systems agree to within 2%. The design of the system is then altered, to improve sensitivity, and the sensitivities of the synthesised and experimental systems are again compared.

Comparative application of the Crank-Nicolson and State-Space methods to the solution of nonlinear instantaneous eddy current and flux penetration problems in electrical machines

Abstract: Two numerical methods are presented and compared for solution of nonlinear instantaneous electromagnetic diffusion problems. Finite differences are used for discretization of space. The Crank-Nicolson and improved State-Space methods are used for time. A magnetic vector potential (m.v.p.) formulation is used, which is effective in simplifying programming implementation to electrical machinery problems with complex contours. The methods are applied to a practical example of eddy currents, flux penetration and losses, and are found to yield results which are in excellent agreement with experimental test data. The results include a vivid display of the distortive effect of magnetic non-linearity on eddy current and flux density wave forms. The comparative suitability of both methods are evaluated in light of their characteristics and results.

A manifestly gauge-invariant hamiltonian formulation of classical electrodynamics including magnetic monopoles

Abstract: The formulation of classical electrodynamics of Balescu and Poulain [Physica 76 (1974) 421] is extended to include magnetic monopoles. It is found that this can be done consistently if we assume a magnetic charge and an electric charge never occupu the same space time point.