Maxwell’s equations in material media, momentum balance equations and force densities associated with them

Jiménez, J. L.; Campos, Irma Manrique; López-Mariño, M. A.

doi:10.1140/epjp/i2013-13046-8

Cited by 10 publications

(16 citation statements)

References 8 publications

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“…We have shown elsewhere [16] [18] that the macroscopic Maxwell equations can be transformed, by means of vector and dyadic identities, into electromagnetic momentum balance equations. These balance equations involve different momentum flux tensors and force densities.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

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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Section: Discussionmentioning

confidence: 99%

“…However, the force expressed in "Equation (18)" is obtained assuming, for paramagnetic and diamagnetic media, that the field H is nearly constant [12] so that…”

mentioning

confidence: 99%

Electrostatic and Magnetostatic Forces That Arise from Electrostatic and Magnetostatic Pressures

Jiménez-Ramírez¹,

Campos-Flores²,

Roa-Neri³

2019

JEMAA

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“…By means of vector and dyad identities these equations can be transformed into the balance equation (Jiménez et al 2011, Jiménez et al 2013)…”

Section: A Maxwellian Approachmentioning

confidence: 99%

The Feynman paradox and hidden momentum

Jiménez¹,

Campos²,

Roa-Neri³

2022

Eur. J. Phys.

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Though it is generally accepted that electromagnetic radiation fields possess energy and linear and angular momentum, the adscription of these properties to static and quasi-static fields rises some doubts. Some authors consider that in electrostatics the concept of field is superfluous, or that action-at-a-distance and field are equivalent views. However, the interpretation of Poynting´s vector divided by c2 as a momentum density is consistent and necessary for the conservation laws to hold, even in static conditions. The Feynman paradox exhibits the necessity of assigning linear and angular momentum to static and quasi-static fields, showing in this way that the points of view of action-at-a-distance and field are not equivalent. In the present work we do not intend to present a revision of the literature on this subject, but to show that the concept of hidden momentum is useful to solve the paradox, and we show that it is part of a momentum balance equation derived directly from the macroscopic Maxwell equations. Another consequence of this balance equation is that, in static conditions, the momentum associated to Poynting´s vector equals the hidden momentum and cancels it. Graduate students and researchers interested in conceptual problems of electromagnetism will find a firm foundation of the concept of hidden momentum and an alternative view of the paradox.

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“…Since Ω is filled with magnetostrictive material, the momentum balances must include mechanic and electromagnetic contributions. The latter will be obtained from the magnetic Maxwell's laws [22] in the absence of j f :…”

Section: Momentum Balancesmentioning

confidence: 99%

Non-linear and hysteretical finite element formulation applied to magnetostrictive materials

2020

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Giant magnetostrictive actuators are suitable for applications requiring large mechanical displacements under low magnetic fields; for instance Terfenol-D made out of rare earth-iron materials can produce important strains. But these actuators exhibit hysteretic non-linear behavior, making it very difficult to experimentally characterize them. Therefore, sophisticated numerical algorithms to develop computational tools are necessary. In this work, theoretical and numerical formulations within the finite element method are developed to simulate magnetostriction. Theoretically, within the framework of non-equilibrium thermodynamics, the hysteresis is introduced by the Debye-memory relaxation. Numerically, the main novelty is the time integration, coupled Newmark-β (for mechanical) and convolution integrals (for magnetic constitutive equations); the non-linearity is solved with the standard Newton-Raphson algorithm. Constitutive non-linearities are incorporated with the Maxwell stress tensor, quadratically dependent on the magnetic field. The numerical code is validated using analytical and experimental solutions; several examples are presented to demonstrate the capabilities of the present formulation.

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Maxwell’s equations in material media, momentum balance equations and force densities associated with them

Cited by 10 publications

References 8 publications

Electrostatic and Magnetostatic Forces That Arise from Electrostatic and Magnetostatic Pressures

Electrostatic and Magnetostatic Forces That Arise from Electrostatic and Magnetostatic Pressures

The Feynman paradox and hidden momentum

Non-linear and hysteretical finite element formulation applied to magnetostrictive materials

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