Browse > Article

On the Physical Meaning of Maxwell Stress Tensor  

Choi, Hong-Soon (경북대학교 전자전기공학부)
Park, Il-Han (성균관대학교 정보통신공학부)
Moon, Won-Kyu (포항공과대학교 기계공학과)
Publication Information
The Transactions of The Korean Institute of Electrical Engineers / v.58, no.4, 2009 , pp. 725-734 More about this Journal
Abstract
Maxwell stress tensor is one of the methods which are generally used for electromagnetic force calculation. In this paper, it is presented that Maxwell stress tensor T and n${\cdot}$T have no physical meaning and therefore should not be used as sources of mechanical force for deformations or dynamics. The divergence of Maxwell stress tensor ${\nabla}{\cdot}T$ is the one which can acquire a physical identity and is electromagnetic body force density by an action at a distance like a gravity. This result can be derived from the principle of power balance, and also verified by some thought experiments. The virtual air-gap approach is proposed as a valid solution for the calculation of the body force.
Keywords
Maxwell stress tensor; Electromagnetic force; Body force; Mechanical stress; Solid mechanics; Mechanical dynamics; Hydrostatics;
Citations & Related Records

Times Cited By SCOPUS : 0
연도 인용수 순위
  • Reference
1 J. A. Stratton, Electromagnetic Theory, New York: McGraw Hill Book Co., 1941
2 A. Bossavit, 'On local computation of the electromagnetic force field in defonnable bodies,' Int. J. Applied Electromagnetics in Materials, 2, 4, pp. 333-343, 1992
3 See Ref [3], pp. xi-xv in the preface
4 J. J. Roche, 'B and H, the intensity vectors of magnetism A new approach to resolving a century-old controversy,' Am. J Phys. 68(5), pp. 163-168, May 2000   DOI   ScienceOn
5 H. S. Choi, I. H. Park, and S. H. Lee, 'Concept of virtual air gap and its application for force calculation,' IEEE Trans. Magn., vol.42, no.4, pp. 663-666, April 2006   DOI   ScienceOn
6 H. S. Choi, Y. S. Kim, K. T. Kim, and I. H. Park, 'Simulation of hydrostatical equilibrium of ferrofluid subjected to magneto-static field,' IEEE Trans. on Magnetics, Vol.44, No.6, pp.818-821, June 2008   DOI   ScienceOn
7 H. S. Choi, S. H. Lee, and I. H. Park, 'Generalized Equivalent Magnetizing Current Method for Total Force Calculation of Magnetized Bodies in Contact.' IEEE Trans. Magn, vol.42, no.4, pp.531-534, April 2006   DOI   ScienceOn
8 C. Rinaldi and H. Brenner, 'Body versus surface forces in continuum mechanics: Is the Maxwell stress tensor a physically objective Cauchy stress?' Physical Review E, Vol. 65, 036615, 2002   DOI
9 H. S. Choi, J. H. Lee, and I. H. Park, 'Separation of each torque component on parts of electric machine using magnetic force density,' IEEE Trans. Magn, vol.41, no.5, pp.1464-1467, May 2005   DOI   ScienceOn
10 R. Aris, Vectors, Tensors. and the Basic Equations of Fluid Mechanics, Dover Publications, New York, 1989
11 See Ref. [8], pp. 100
12 J. Slepian, 'Electromagnetic ponderomotive forces within material bodies,' Proc. Nat. Acad. Sci., vol. 36, no. 9, pp. 485-497, Sep. 1950   DOI   ScienceOn
13 See Ref. [1], pp. 97-103
14 A. DiCarlo, 'G. Lame vs. J, C, Maxwell: How to Reconcile Them?' Proc. of Scientific Computing in Electrical Eng., pp. 1-13, June 2002
15 S. Bobbio, Electrodynamics of Materials: Forces, Stresses, and Energies in Solids and Fluids, Academic Press, 2000
16 H. S. Choi, S. H. Lee, and I. H. Park, 'Electromagnetic body force calculation based on virtual air-gap,' Journal of Applied Physics 99, 08H903, 2006   DOI   ScienceOn
17 H. S. Choi, Y. S. Kim, J. H. Lee, and 1. H. Park, 'An Observation of Body Force Distributions in Electric Machines', IEEE Trans. on Magnetics, VoI.43, No.4, pp.1861-1864, April 2007   DOI   ScienceOn
18 민만기, 서이수, '자성유체의 물리적 성질과 그의 응용,' 대한기계학회지, 30권, 2호, pp.188-193, 1990   과학기술학회마을
19 K. Reichert, H. Freundl, and W. Vogt, 'The calculation of force and torque within numerical magnetic field calculation method,' Proceedings on COMPUMAG, pp.64-74, 1976
20 H. A. Haus and J. R. Melcher, Electromagnetic Fields and Energy, London: Prentice-Hall, 1989, pp. 504-510
21 H. S. Choi , S. H. Lee, and I. H. Park, 'General fonnulation of equivalent magnetic charge method for force density distribution on interface of different materials,' IEEE Trans. Magn., vol.41, no.5, pp. 1420-1423, May 2005   DOI   ScienceOn
22 H. S. Choi, S. H. Lee. Y. S. Kim, K. T. Kim, and I. H. Park, 'Implementation of Virtual Work Principle in Virtual Air Gap,' IEEE Trans. on Magnetics, Vol.44, No.6, pp.1286-1289, June 2008   DOI   ScienceOn
23 R. E. Rosensweig, Ferrohydrodynamics, New York: Dover, 1997