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scientific edition of Bauman MSTU


Bauman Moscow State Technical University.   El № FS 77 - 48211.   ISSN 1994-0408

On the Basic Equations of the Magnetostatics

# 05, May 2016
DOI: 10.7463/0516.0840425
Article file: SE-BMSTU...o139.pdf (1234.48Kb)
authors: A.M. Makarov1,*, L.A. Luneva1, K.A. Makarov1

1 Bauman Moscow State Technical University, Moscow, Russia

The paper studies the physical relationship between the main objects of the magnetic field in a continuous medium with magnetization effects. Consistently considers the following hypotheses: a hypothesis of the primacy and the physical reality of the magnetization vector field environment, a similar hypothesis about the real existence of Ampere currents (molecular currents, magnetization currents), a hypothesis of a magnetic dipole moment of the medium volume element in view of bulk density of electric currents in this volume. A more rigorous derivation of the basic differential equations of magnetostatics from the Biot-Savart-Laplace equation is proposed.
The well-known works justifying basic equations of magnetostatics use a procedure wherein when proving the local differential ratio is used a transformation of some volume integral to the surface integral bounding this volume. Thus, there is a specific way to select a  closed surface that is either a surface in a vacuum (beyond the medium volume under consideration), or a surface of the conductor (a normal component of currents to the surface, here, becomes zero). In the paper the control surface is arbitrarily carried out within the volume of the medium under consideration, thereby leading to the mathematically sound result.
The paper analyzes the hypotheses listed above. The main feature of analysis is a succesively using concept of bilateralism surface bounding the medium volume of the  arbitrary finite dimensions. The analysis allowed us to reveal the physical adequacy of the considered hypotheses, derive the appropriate differential equations for the basic vector fields of magnetostatics and obtain a new condition. The resulting condition for the closedness of magnetization currents is recorded in entire compliance with the well-known Gauss electrostatic law, which avoids the need for additional, but not always reasonable assumptions.

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