Maxwellian stresses and electromagnetic forces that arise from them in vacuum and media.

I. Campos Flores, J. L. Jiménez Ramírez, J. A. E. Roa Neri

Abstract


Faraday and Maxwell conceived the electrostatic and magnetostatic fields as lines of force filling the space around charges and currents, with or without matter. They also established that there are tensions along the lines of force, and compressions around these lines. These ideas are formalized with a stress tensor, whose divergence is a force density. We follow these ideas to show the origin of the electric forces that arise in the case of a dielectric slab partially introduced into a parallel-plate capacitor, and the origin of the magnetic forces that arise in the case of a magnetizable bar partially introduced into a solenoid. We find that these forces have their origin in the abrupt change in permittivity and permeability which produce a difference of pressures at interfaces. This approach permits us to analyze the similarities and differences between both cases. Advanced undergraduate and graduate students can get interesting insights into the electromagnetic forces exerted by electrostatic and magnetostatic fields in vacuum and matter. 

 

Faraday y Maxwell concibieron los campos electrostáticos y magnetostáticos como líneas de fuerza llenando el espacio alrededor de cargas y corriente, con o sin materia. Ellos establecieron que hay tensiones a lo largo de las líneas de fuerza, y compresiones alrededor de estas líneas. Estas ideas se formalizan con el tensor de esfuerzos, cuya divergencia es una densidad de fuerza. Nosotros seguimos estas ideas para mostrar el origen de las fuerzas eléctricas que surgen cuando una barra de dieléctrico se introduce parcialmente en un condensador de placas paralelas, y el origen de las fuerzas magnéticas que surgen en el caso de una barra magnetizable parcialmente introducida en un solenoide. Encontramos que estas fuerzas tienen su origen en el cambio abrupto en la permitividad y permeabilidad que produce una diferencia de presiones en la interface. Este enfoque  nos permite analizar las similitudes y diferencias entre ambos casos. Los estudiantes no graduados y graduados pueden adquirir una percepción interesante  sobre las fuerzas electromagnéticas ejercidas por campos electrostáticos y magnetostáticos en el vacío y en la materia


Keywords


Maxwell equations; Electromagnetic balance equations; Maxwell stresses; Electromagnetic force densities

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References


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DOI: https://doi.org/10.31349/RevMexFisE.18.3

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REVISTA MEXICANA DE FÍSICA E, year 18, issue 1, January-June 2021. Semiannual Journal published by Sociedad Mexicana de Física, A. C. Departamento de Física, 2º Piso, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Alcaldía Coyacán, C.P. 04510 , Ciudad de México. Apartado Postal 70-348. Tel. (+52)55-5622-4946, https://rmf.smf.mx/ojs/rmf-e, rmf@ciencias.unam.mx. Chief Editor: José Alejandro Ayala Mercado.  INDAUTOR Certificate of Reserve: 04-2019-080216402500-203, ISSN: 2683-2216 (on line), 1870-3542 (print), both granted by Instituto Nacional del Derecho de Autor.  Responsible for the last update of this issue, Technical Staff of Sociedad Mexicana de Física, A. C., Fís. Efraín Garrido Román, 2º. Piso, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Alcaldía Coyacán, C.P. 04510 , Ciudad de México. Date of last modification, January 04, 2021.

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