Anisotropy component of electromagnetic force and torque

Abstract

The paper deals with the problem of surface-integral representation of electromagnetic force/torque for magnetically anisotropic region. It is pointed out that in some anisotropic regions a component of electromagnetic force/torque appears-the so-called anisotropy component. The total electromagnetic field force/torque calculated with the help of Maxwell's and Lorentz's methods could lead to the different values for some anisotropic medium (homogeneous, without hysteresis). The coenergy method is used to evaluate total force/torque too. Analytical calculations of force/torque for isotropic and anisotropic media in electromagnetic field are presented. The condition for surface integral representation of Lorentz's either force or torque is formulated.

Electrostatic and magnetostatic levitations of ball – forces, stability and oscillations frequencies

“…Material forces appear at the boundary when object permeability is different from the outside permeability. It is assumed that no forces are exerted by magnetic hysteresis, magnets, and magnetic asymmetric anisotropy [5, 13, 14, 17, 20 ].…”

“…The novelty of the analytical solutions derived lays in considering – material forces arising at the surface of balls described mathematically by inhomogeneity component [12, 16 ], – dielectric and magnetic anisotropy (normal in a spherical coordinate system) of levitating balls [17 ], – extension (in comparison with [2, 3 ]) of forced fields class in the form of polynomials (1 ) and (27 ), – analysis of vertical levitations stability, and – evaluation of oscillation frequencies. …”

Two theorems about Lorentz method for asymmetrical anisotropic regions

“…The electromagnetic field forces [1,2] theoretical analysis is still a vital problem [3][4][5]. For evaluation of the electromagnetic force density the following form is applied…”

“…where M is so-called anisotropy component [4,5]. The proof of (1) bases on the Lorentz force density f L formula, Maxwell's equations, and assumptions that displacement current (that leads to electromagnetic field impulse force [5,6]) and hysteresis phenomenon can be neglected (nonhomogeneous component N = 0). The force density component M in (1) means the anisotropy force component.…”

“…where i u denotes versor for u th coordinate, vectors σ u (u = 1, 2, 3) are built of Maxwell's stress tensors and ∆ is the residual vector [4,5]. The total force or torque can also be calculated by means of the coenergy method.…”