
-
Previous Article
Analysis of discretized parabolic problems modeling electrostatic micro-electromechanical systems
- DCDS-S Home
- This Issue
-
Next Article
Formal asymptotic analysis of elastic beams and thin-walled beams: A derivation of the Vlassov equations and their generalization to the anisotropic heterogeneous case
Magnetic forces in and on a magnet
Laboratoire de Génie électrique et électronique de Paris (GeePs), Universities UPMC and UPSud, Gif-sur-Yvette, France |
Given the shape of a magnet and its magnetization, point by point, which force does it exert on itself, also point by point? We explain what 'force' means in such a context and how to define it by using the Virtual Power Principle. Mathematically speaking, this force is a vector-valued distribution, with Dirac-like concentrations on surfaces across which the magnetization is discontinuous, i.e., material interfaces. To find these concentrations, we express the force as the divergence of a (symmetric) 2-tensor which generalizes a little the classical Maxwell tensor.
References:
[1] |
J. G. van Bladel, Unusual boundary conditions at an interface, IEEE A.P. Mag., 33 (1991), 57-58. Google Scholar |
[2] |
A. Bossavit, Forces inside a magnet, Int. Compumag Soc. Newsletter, 11 (2004), 4-12. Google Scholar |
[3] |
A. Bossavit, Bulk forces and interface forces in assemblies of magnetized pieces of matter, IEEE Trans. Magn., 52 (2016), Art. 7003504. Google Scholar |
[4] |
H. S. Choi, I. H. Park and S. H. Lee, Concept of virtual airgap and its application for forces computations, IEEE Trans. Magn., 42 (2006), 663-666. Google Scholar |
[5] |
H. Gouin and J.-F. Debieve, Variational principle involving the stress tensor in elastodynamics, Int. J. Engng Sc., 24 (1986), 1057-1066. Google Scholar |
[6] |
E. Kröner, Benefits and shortcomings of the continuous theory of dislocations, Int. J. Solids & Structures, 38 (2001), 1115-1134. Google Scholar |
[7] |
A. R. Lee and T. M. Kalotas, A note on unconventional Gaussian surfaces, Am. J. Phys., 54 (1986), 753-754. Google Scholar |
[8] |
J. E. Marsden and T. J. Hughes, Mathematical Foundations of Elasticity, Prentice Hall, Englewood Cliffs, 1983. Google Scholar |
[9] |
P. Penfield Jr., Hamilton's principle for fluids, Phys. Fluids, 9 (1966), 1184-1194. Google Scholar |
[10] |
K. Reichert, H. Freundl and W. Vogt, The calculation of forces and torques within numerical magnetic field calculation methods, Compumag, (1976), 64-73. Google Scholar |
[11] |
W. G. V. Rosser, Classical Electromagnetism via Relativity, An Alternative Approach to Maxwell's Equations, Butterworths, London, 1968. Google Scholar |
[12] |
J. M. Souriau,
Physics and geometry, Found. Phys., 13 (1983), 133-151.
doi: 10.1007/BF01889416. |
[13] |
A. N. Wignall, A. J. Gilbert and S. J. Yang, Calculation of forces on magnetised ferrous cores using the Maxwell stress tensor, IEEE Trans. Magn., 24 (1988), 459-462. Google Scholar |
show all references
References:
[1] |
J. G. van Bladel, Unusual boundary conditions at an interface, IEEE A.P. Mag., 33 (1991), 57-58. Google Scholar |
[2] |
A. Bossavit, Forces inside a magnet, Int. Compumag Soc. Newsletter, 11 (2004), 4-12. Google Scholar |
[3] |
A. Bossavit, Bulk forces and interface forces in assemblies of magnetized pieces of matter, IEEE Trans. Magn., 52 (2016), Art. 7003504. Google Scholar |
[4] |
H. S. Choi, I. H. Park and S. H. Lee, Concept of virtual airgap and its application for forces computations, IEEE Trans. Magn., 42 (2006), 663-666. Google Scholar |
[5] |
H. Gouin and J.-F. Debieve, Variational principle involving the stress tensor in elastodynamics, Int. J. Engng Sc., 24 (1986), 1057-1066. Google Scholar |
[6] |
E. Kröner, Benefits and shortcomings of the continuous theory of dislocations, Int. J. Solids & Structures, 38 (2001), 1115-1134. Google Scholar |
[7] |
A. R. Lee and T. M. Kalotas, A note on unconventional Gaussian surfaces, Am. J. Phys., 54 (1986), 753-754. Google Scholar |
[8] |
J. E. Marsden and T. J. Hughes, Mathematical Foundations of Elasticity, Prentice Hall, Englewood Cliffs, 1983. Google Scholar |
[9] |
P. Penfield Jr., Hamilton's principle for fluids, Phys. Fluids, 9 (1966), 1184-1194. Google Scholar |
[10] |
K. Reichert, H. Freundl and W. Vogt, The calculation of forces and torques within numerical magnetic field calculation methods, Compumag, (1976), 64-73. Google Scholar |
[11] |
W. G. V. Rosser, Classical Electromagnetism via Relativity, An Alternative Approach to Maxwell's Equations, Butterworths, London, 1968. Google Scholar |
[12] |
J. M. Souriau,
Physics and geometry, Found. Phys., 13 (1983), 133-151.
doi: 10.1007/BF01889416. |
[13] |
A. N. Wignall, A. J. Gilbert and S. J. Yang, Calculation of forces on magnetised ferrous cores using the Maxwell stress tensor, IEEE Trans. Magn., 24 (1988), 459-462. Google Scholar |

[1] |
Roland Schnaubelt, Martin Spitz. Local wellposedness of quasilinear Maxwell equations with absorbing boundary conditions. Evolution Equations & Control Theory, 2021, 10 (1) : 155-198. doi: 10.3934/eect.2020061 |
[2] |
Giuseppe Capobianco, Tom Winandy, Simon R. Eugster. The principle of virtual work and Hamilton's principle on Galilean manifolds. Journal of Geometric Mechanics, 2021 doi: 10.3934/jgm.2021002 |
[3] |
Marion Darbas, Jérémy Heleine, Stephanie Lohrengel. Numerical resolution by the quasi-reversibility method of a data completion problem for Maxwell's equations. Inverse Problems & Imaging, 2020, 14 (6) : 1107-1133. doi: 10.3934/ipi.2020056 |
[4] |
Yue-Jun Peng, Shu Wang. Asymptotic expansions in two-fluid compressible Euler-Maxwell equations with small parameters. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 415-433. doi: 10.3934/dcds.2009.23.415 |
[5] |
Xing-Bin Pan. Variational and operator methods for Maxwell-Stokes system. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3909-3955. doi: 10.3934/dcds.2020036 |
[6] |
Pierre-Etienne Druet. A theory of generalised solutions for ideal gas mixtures with Maxwell-Stefan diffusion. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020458 |
[7] |
Chungen Liu, Huabo Zhang. Ground state and nodal solutions for fractional Schrödinger-maxwell-kirchhoff systems with pure critical growth nonlinearity. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020292 |
[8] |
Fabio Camilli, Giulia Cavagnari, Raul De Maio, Benedetto Piccoli. Superposition principle and schemes for measure differential equations. Kinetic & Related Models, 2021, 14 (1) : 89-113. doi: 10.3934/krm.2020050 |
[9] |
Cung The Anh, Dang Thi Phuong Thanh, Nguyen Duong Toan. Uniform attractors of 3D Navier-Stokes-Voigt equations with memory and singularly oscillating external forces. Evolution Equations & Control Theory, 2021, 10 (1) : 1-23. doi: 10.3934/eect.2020039 |
[10] |
Noriyoshi Fukaya. Uniqueness and nondegeneracy of ground states for nonlinear Schrödinger equations with attractive inverse-power potential. Communications on Pure & Applied Analysis, 2021, 20 (1) : 121-143. doi: 10.3934/cpaa.2020260 |
[11] |
Stefan Doboszczak, Manil T. Mohan, Sivaguru S. Sritharan. Pontryagin maximum principle for the optimal control of linearized compressible navier-stokes equations with state constraints. Evolution Equations & Control Theory, 2020 doi: 10.3934/eect.2020110 |
[12] |
Meng Ding, Ting-Zhu Huang, Xi-Le Zhao, Michael K. Ng, Tian-Hui Ma. Tensor train rank minimization with nonlocal self-similarity for tensor completion. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2021001 |
[13] |
Claudianor O. Alves, Rodrigo C. M. Nemer, Sergio H. Monari Soares. The use of the Morse theory to estimate the number of nontrivial solutions of a nonlinear Schrödinger equation with a magnetic field. Communications on Pure & Applied Analysis, 2021, 20 (1) : 449-465. doi: 10.3934/cpaa.2020276 |
[14] |
Giuseppina Guatteri, Federica Masiero. Stochastic maximum principle for problems with delay with dependence on the past through general measures. Mathematical Control & Related Fields, 2020 doi: 10.3934/mcrf.2020048 |
[15] |
Puneet Pasricha, Anubha Goel. Pricing power exchange options with hawkes jump diffusion processes. Journal of Industrial & Management Optimization, 2021, 17 (1) : 133-149. doi: 10.3934/jimo.2019103 |
[16] |
Gang Luo, Qingzhi Yang. The point-wise convergence of shifted symmetric higher order power method. Journal of Industrial & Management Optimization, 2021, 17 (1) : 357-368. doi: 10.3934/jimo.2019115 |
[17] |
Kai Zhang, Xiaoqi Yang, Song Wang. Solution method for discrete double obstacle problems based on a power penalty approach. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2021018 |
[18] |
Tomáš Oberhuber, Tomáš Dytrych, Kristina D. Launey, Daniel Langr, Jerry P. Draayer. Transformation of a Nucleon-Nucleon potential operator into its SU(3) tensor form using GPUs. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 1111-1122. doi: 10.3934/dcdss.2020383 |
[19] |
Feimin Zhong, Jinxing Xie, Yuwei Shen. Bargaining in a multi-echelon supply chain with power structure: KS solution vs. Nash solution. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2020172 |
[20] |
Gunther Uhlmann, Jian Zhai. Inverse problems for nonlinear hyperbolic equations. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 455-469. doi: 10.3934/dcds.2020380 |
2019 Impact Factor: 1.233
Tools
Metrics
Other articles
by authors
[Back to Top]