A New Perspective of the Force on a Magnetizable Rod inside a Solenoid

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

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“…applicable in the case of a non-uniform H field. It has been shown elsewhere [23] that the force density Eq. (52) leads to the known result, Eq.…”

Section: Magnetostatic Forces In Materials Mediamentioning

confidence: 94%

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

2021

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Electrostatic and Magnetostatic Forces That Arise from Electrostatic and Magnetostatic Pressures

Jiménez-Ramírez¹,

Campos-Flores²,

Roa-Neri³

2019

JEMAA

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With the insight provided by a balance equation of electromagnetic momentum, we compare the force on a dielectric slab inside a capacitor with the force on a magnetizable rod inside a solenoid. We conclude that these forces are not exactly analogous, as usually thought. We present a device that is a proper analogy of the case of a dielectric slab inside a capacitor. Our analysis shows the significance of the electrostatic and magnetostatic pressures to the understanding of these effects and shows the conceptual differences between both cases.

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A New Perspective of the Force on a Magnetizable Rod inside a Solenoid

Cited by 2 publications

References 13 publications

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

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

Electrostatic and Magnetostatic Forces That Arise from Electrostatic and Magnetostatic Pressures

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