A Short Review of Electromagnetic Force Models for Matter - Theory and Experimental Evidence

  • Wilhelm RickertEmail author
  • Wolfgang Müller
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 100)


From Maxwell’s equations balance laws for the electromagnetic linearmomentum, angular momentum, and energy can be found after recasting and usingseveral identities of vector calculus. Therefore, the obtained equations are not “newresults” but rather identities having the form of a balance law. However, there is some degree of freedom, (a) during construction of a particular identity and (b) for the choice of the to-be-balanced quantity, the non-convective flux, and the production term. In short, one is insecure which of the various forms is correct under which circumstances. This conundrum is referred to as the Abraham-Minkowski controversy, who first proposed different expressions for the electromagnetic linear momentum. The proper choice of electromagnetic force and torque expressions is of particular importance in matter where the mechanical and electromagnetic fields couple. The question arises as to whether a comparison between the predicted deformation behavior and the observed one can help to decide which electromagnetic force model is suitable for a material of interest. In this paper we shall briefly review the controversy and suggest new approaches for its solution on the continuum level.


Electromagnetic force models Magnetostriction Electrostriction Total forces and torques 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institut für Mechanik, Kontinuumsmechanik und MaterialtheorieTechnische Universität BerlinBerlinGermany

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