Two Theorems About Surface-Integral Representation of Electromagnetic Force and Torque

Spałek, D.

doi:10.1109/tmag.2016.2636208

Cited by 3 publications

(7 citation statements)

References 9 publications

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“…c) Physically, the electrostatic levitation force is driven by material force F Nz acting only at the surface of the ball where the electric permittivity changes in step way (the material force density is equal to zero inside the homogeneous ball). Mathematically, the levitation force describes the inhomogeneity component [5, 12, 13, 16, 20 ]. The inhomogeneous component describes the material force density (acting on dielectric) as follows:

N = - \frac{1}{2} E_{u} E_{w} normalgrad (ε_{u w}),

where dummy index summation is implied (i.e.…”

Section: Electrostatic Levitationmentioning

confidence: 99%

“…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 ].…”

Section: Magnetostatic Levitationmentioning

confidence: 99%

“…The paper considers both electrostatic and magnetostatic levitations driven only by material forces acting on dielectric, paramagnetic, and ferromagnetic materials. Static levitation forces act either separately [1, 7, 8 ] or together with other electromagnetic forces ([2, 4, 11–13 ] and Table 1 ).…”

Section: Introductionmentioning

confidence: 99%

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

Spałek

2020

IET Science, Measurement &Amp; Technology

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The study presents approaches to both electrostatic and magnetostatic levitations. For anisotropic balls, both dielectric and magnetic field distributions are derived in analytical forms by means of the variable separation method. Distributions are given by power functions and polynomials either Legendre's (for the electrostatic problem) or the associated polynomials (for the magnetostatic problem). The levitation forces are evaluated by means of four methods, i.e. Maxwell stress tensor generalised method, co‐energy method, material force density, and equivalent dipole analysis for both levitations. Levitation forces versus either electric permittivity or magnetic permeability are presented. The stability of the equilibrium points is investigated. The frequencies of free and damped oscillations are evaluated.

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N = - \frac{1}{2} E_{u} E_{w} normalgrad (ε_{u w}),

where dummy index summation is implied (i.e.…”

Section: Electrostatic Levitationmentioning

confidence: 99%

Section: Magnetostatic Levitationmentioning

confidence: 99%

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

Spałek

2020

IET Science, Measurement &Amp; Technology

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“…Electromagnetic levitation (of induced currents) and/or magnetic levitation (of magnetic matter) could lift an object in a Particularly, the levitation could be caused by: • Lorentz force acting upon currents induced in a conductive probe (electromagnetic levitation, power losses [7,8]); • Material forces acting on the outer surface and/or inside an object, i.e. in regions where magnetic reluctivity changes [8][9][10][11][12] as well as (not considered in this paper):…”

Section: Electromagnetic and Magnetic Levitationsmentioning

confidence: 99%

“…Both the Lorentz and material forces lift the conductive and magnetic object if their sum is greater than the gravitational force mg (weight). Furthermore, it is assumed that forces exerted by magnetic hysteresis, magnets, and magnetic asymmetrical anisotropy do not appear [1,2,11,[13][14][15][16]. The Lorentz force is immanently bound up with the Joule power losses.…”

Section: Electromagnetic Field Analysismentioning

confidence: 99%

Bulletin of the Polish Academy of Sciences: Technical Sciences

Spałek

2020

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The paper presents an analytical solution of levitation problem for conductive, dielectric and magnetically anisotropic ball. The levitation exerts either an AC or impulse magnetic field. Both the Lorentz and material electromagnetic forces (of magnetic matter) could lift the ball in a gravitational field. The electromagnetic field distribution is derived by means of variables separation method. The total force is evaluated by Maxwell stress tensor (generalized), co-energy and Lorentz methods. Additionally, power losses are calculated by means of Joule density and the Poynting vector surface integrals. High frequency asymptotic formulas for the Lorentz force and power losses are presented. All analytical solutions derived could be useful for rapid analysis and design of levitations systems. Finally, some remarks about considered levitations are formulated.

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Electrostatic levitations of anisotropic dielectric oblate and prolate spheroids

Spałek

2023

Electr Eng

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The paper presents analytical approach to electrostatic field for dielectric spheroids problem. For both oblate and prolate spheroids fields distributions are derived. The variable separation method is applied. Electrostatic force is evaluated with the help of the Maxwell stress tensor generalized method, material force density, coenergy and equivalent dipole. Levitation forces for both oblate and prolate dielectric spheroids versus axis permittivities and spheroids height are presented.

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Two Theorems About Surface-Integral Representation of Electromagnetic Force and Torque

Cited by 3 publications

References 9 publications

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

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

Bulletin of the Polish Academy of Sciences: Technical Sciences

Electrostatic levitations of anisotropic dielectric oblate and prolate spheroids

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