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Konstantin E. Voevodskii, Vladimir M. Strepetov
St. Petersburg State University Emperor Alexander I Petersburg State Transport University

THE METHOD OF CONDITIONAL BOUNDAR

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Abstract: The goal of this work is to propose a new approach to the calculation of electromagnetic field that excited by the eddy current induced in the conductive environment the influence of an external magnetic field source. The quasistationary approximation accepted, that is, the bias currents do not take into account.

Method. The main feature of the method is the introduction of so-called conditional boundary. This name is given for mental surfaces, which can be done in the area, free of conductive environment. Boundary form is arbitrary and dictated by considerations of calculations convenience. The agreement that the same boundary conditions, like on the conductor-vacuum boundary are performed.

We prove that this task change leads to a change in its decisions only outside of the conductor and the only for part of the electric field. Magnetic induction vector throughout the space, as well as electric field tension vector in the conductive environment do not change.

At the same time, a good choice of conditional boundary in some cases allows to simplify the task with calculation point of view.

In addition to the conditional boundaries introduction, some formal basic conversion ratios are proposed, describing quasistationary electromagnetic field. These changes had the same goal to simplify calculations.

The result. The new formulation of task of quasistationary electromagnetic field calculation is received in the form of differential equations system and boundary conditions, including both known ratio and the newly received. The new formulation is equivalent to traditional (with the above proviso). However, it has some advantages in terms of ease of calculation.

The practical significance. In practice of specific calculations the method would be useful, particularly in cases when the form guide is close to some "simple" form.

Keywords: conditional boundary, electromagnetic field, eddy current, conductive environment, boundary conditions, harmonic function, boundary value problem, a simple layer potential, generalized functions, singularity, quasistationary approximation.

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