A Magnetic Field Diffusion Problem (1969)

European Journal of Physics, 1998

Assuming given externally applied magnetic fields and given velocities, we calculate the currents induced in moving conductors of arbitrary conductivity, and the net magnetic field. Three of the four conductors are solid, and the fourth is fluid. We find that, in these examples, the net magnetic field is either unaffected by the moving conductor, or distorted downstream, or distorted upstream. In all cases the net magnetic field is static.

Geophysical and Astrophysical Fluid Dynamics, 2005

Diffusion of a magnetic field through a plasma is discussed in one-, two- and three-dimensional configurations, together with the possibility of describing such diffusion in terms of a magnetic flux velocity, which, when it exists, is in general non-unique. Physically useful definitions of such a velocity include doing so in terms of the energy flow or in such a way

IEEE Transactions on Magnetics, 2015

The present paper provides the 3-D time-dependent analytical solution of the electromagnetic fields and forces emerging if a coil or a permanent magnet moves with a sinusoidal velocity profile relative to a conducting slab of finite thickness. The results can be readily used in application scenarios related to electromagnetic damping, eddy current braking, energy harvesting or nondestructive testing in order to efficiently analyze diffusion and advection processes in case of harmonic motion. The study is performed for rectangular and circular coils as well as for cuboidal and cylindrical permanent magnets. The back reaction of the conductor and therewith associated inductive effects are considered. The solutions of the governing equations and the integral expressions for the time-dependent drag-and lift-force are provided. The analytical results are verified by a comparison to numerical simulations obtained by the finite-element method. The relative difference between the analytically and numerically evaluated force profiles was < 0.1%. Exemplary calculations show that the waveforms of both force components strongly depend on the level of constant nominal velocity v0, the magnitude of the velocity oscillation amplitude v1 and the underlying oscillation frequency fv. His current research interests include numerical simulations and visualization of electromagnetic fields, with applications to forward/inverse problems in nondestructive evaluation, bioelectromagnetics, small electrical machines, and magnetic fluid dynamics.

European Journal of Physics, 2013

The electric and magnetic fields of an infinite straight wire carrying a steady current which is turned on abruptly are determined using Jefimenko's equations, starting from the standard assumption that the wire is electrically neutral in its rest frame. Some nontrivial aspects of the solution are discussed in detail. * This fact is perhaps more transparent when using ∇ × B = ∇(∇ • A) − ∇ 2 A and recognizing that for A expressed by equation (6), ∇ 2 (ln s) appears explicitly in the calculation of ∇ 2 A. ♯ Strictly speaking, the limit here and in (30) is the weak limit (cf., e.g., [8]) and the Laplacian in (26) is the generalized (distributional) one (cf., e.g., [12]).

Currents are established on the surface of conductors by the propagation of electromagnetic waves in the insulating material between them. If the load is less than the characteristic impedance of the insulating material of the line, multiple reflections and retransmissions eventually build up the line current to that required by the load. The currents are initially established on the surface of the conductors before diffusing relatively slowly into the interior and gives rise to the skin effect. The diffusion velocity depends the conductivity, permeability, thickness of the conductor, and the frequency of the excitation, and such effects of the diffusion process are difficult to conceptually appreciate. Fortunately, the diffusion of heat into solids is very similar, and will be used as an analogy to aid understanding. This diffusion is the means whereby current moves into conductors and flux into of magnetic cores. µ ….. (3c)

European Journal of Physics, 2004

Progress In Electromagnetics Research Letters, 2013

Electromagnetic fields associated with the electric current flowing along a horizontal conductor located over perfectly conducting ground are estimated using electromagnetic fields pertinent to acceleration of electric charges. It is shown that the electric and magnetic fields that exist below a long overhead horizontal conductor are nothing but the radiation fields generated by the acceleration of charge at the point of injection of current into the horizontal conductor.

The analysis of the motion of a system of solid conductors in the presence of magnetic fields is performed by solving the classical mechanics equation of motion under the action of magnetic forces. Application of the eddy-current integral equation and the usage of the local coordinates attached to the bodies in motion allow the determination of electromagnetic field without being necessary to reconstruct the discretization grid at each new position of the conducting bodies. Only the submatrices associated with the coupling between the bodies in relative motion are modified in the global system matrix. A time-domain method of solution is first presented for the electromagnetic field problem, coupled with the equation of motion, which can be efficiently applied at high frequencies when the time steps are small. The eddy-current integral equation for the derivative of current density contains a term that takes into account the relative motion of the bodies. Since the electromagnetic quantities vary much more rapidly than the mechanical quantities, a second method is also proposed in this paper, where the eddy-current integral equation is solved in the frequency domain by assuming that the bodies are motionless, but by adding supplementary terms due to the actual motion of the bodies. Thus, only the average force over a period of time is now computed. This method is extremely efficient especially at higher frequencies when the time steps are very small.

In the high-frequency and surge analysis, several approximate expressions are often used for the partial inductance of horizontal and vertical buried conductors in semi-infinite conducting medium. Some of them neglect the effects of the earth surface while other are based on the image theory. Recently, efforts have been made to improve the inductance calculations for buried conductors by using exact expressions for the magnetic field of dc horizontal and vertical electric dipole in semi-infinite conducting medium. Such approach accurately takes into account the effects of the conducting and non-conducting medium boundary. New expressions for partial inductance of horizontal buried conductor were derived. Here we apply similar approach to derive the partial inductance for vertical buried conductor. We also provide details on the inductance calculations for loop inductance of rectangular loop in a semi-infinite conducting medium, considering horizontal and vertical orientation as a two extreme cases. Results indicate that the partial inductances for horizontal and vertical conductor are significantly influenced by the depth of burial,while the loop inductance remains constant regardless of the depth of burial and orientation of the buried loop.

2013

Abstract. The study of magnetic fields produced by steady currents is a full-valued physical theory which like any other physical theory employs a certain mathematics. This theory has two limiting cases in which source of the field is confined on a surface or a curve. It turns out that mathematical methods to be used in these cases are completely different and differ from from that of the main of the main part of this theory, so, magnetostatics actually consists of three distinct theories. In this work, these three theories are discussed with special attention to the case current carried by a curve. In this case the source serves as a model of thin wire carrying direct current, therefore this theory can be termed magnetostatics of thin wires. The only mathematical method used in this theory till now, is the method of Green’s functions. Critical analysis of this method completed in this work, shows that application of this method to the equation for vector potential of a given curren...