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September 29, 2025Open Access

Multipole Distributions and Hyper-Flux Fields

VGVladimir Gol’dshteinBen-Gurion University of the Negev RSReuven Segev

Key Points

Multipole distributions allow for simple calculations of bound charges, enhancing understanding of continuum mechanics.
The framework provides a general expression for mechanical force acting on bodies containing properties like electric charge.
Hyper-fluxes arise from moving multipoles, including diélectrics, which have implications for advanced mechanical theories.
A potential function facilitates the derivation of mechanical forces associated with various properties in this context.

Abstract

We outline here a simple mathematical introduction to the notions of multipoles for a general extensive property from the point of view of continuum mechanics. Classically, is the electric charge, but the theory is not limited to electrostatics. The proposed framework allows a simple computation of the bound "charges" and bound multipoles of lower orders. In addition, if the property has a potential function in the sense described below, a general expression for the mechanical force (power) functional acting on bodies containing the property is presented. Finally, using a similar viewpoint, we consider hyper-fluxes -- flux fields of tensorial order greater than one -- and show that moving multipoles (in particular, a moving dielectric) give rise to hyper-fluxes.

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