Derivation of Coulomb's Law Based on a Mechanical Model of Electromagnetic Field and a Spherical Source and Sink Model of Electric Charges

Mapping Intimacies ◽

10.20944/preprints202101.0453.v1 ◽

2021 ◽

Author(s):

Xiao-Song Wang

Keyword(s):

Electromagnetic Field ◽

Relaxation Time ◽

Time Scale ◽

Mechanical Model ◽

Reduced Form ◽

Spherical Source ◽

Coulomb’S Law ◽

Spherical Sink ◽

Coulomb's Law ◽

Source And Sink

We suppose that vacuum is filled with a kind of continuously distributed matter which may be called the $\Omega(1)$ substratum, or the electromagnetic aether. Suppose that the time scale of a macroscopic observer is very large compares to the the Maxwelllian relaxation time of the $\Omega(1)$ substratum. Thus, the macroscopic observer concludes that the $\Omega(1)$ substratum behaves like a Newtonian-fluid. Inspired by H. A. Lorentz, we speculate that electric charges may be extremely small hard spherical sources or spherical sinks with finite radii. Based on the spherical source and spherical sink model of electric charges, we derive Coulomb's law of interactions between static electric charges in vacuum. Further, we derive a reduced form of the Lorentz's force law for static electric charges in vacuum.

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A piezoelectric contact problem with slip dependent friction and damage

Journal of Applied Analysis ◽

10.1515/jaa-2020-2034 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Abderrezak Kasri

Keyword(s):

Weak Solution ◽

Contact Problem ◽

Dry Friction ◽

Existence And Uniqueness ◽

Variational Formulation ◽

Normal Compliance ◽

Electrically Conductive ◽

Coulomb’S Law ◽

Electrical Condition ◽

Coulomb's Law

Abstract The aim of this paper is to study a quasistatic contact problem between an electro-elastic viscoplastic body with damage and an electrically conductive foundation. The contact is modelled with an electrical condition, normal compliance and the associated version of Coulomb’s law of dry friction in which slip dependent friction is included. We derive a variational formulation for the model and, under a smallness assumption, we prove the existence and uniqueness of a weak solution.

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Innovative Method of Urban Planning Management Based on the Mathematical Modelling of the Network Objects

MATEC Web of Conferences ◽

10.1051/matecconf/201825103040 ◽

2018 ◽

Vol 251 ◽

pp. 03040

Author(s):

Dmitriy Anufriev ◽

Olga Shikulskaya ◽

Mikhail Shikulskiy ◽

Alyona Naberezhnaya

Keyword(s):

Urban Planning ◽

Mathematical Modelling ◽

Retail Trade ◽

Factors Affecting ◽

Innovative Method ◽

Coulomb’S Law ◽

Urban Planning Management ◽

Coulomb's Law

When urban planning for convenience of the population and business it is necessary to place rationally objects of retail trade and service. Currently a large number of different methods are available to achievement of this purpose, but they are not universal. The most effective solutions could be achieved through the transfer of laws from one area of knowledge to another. The Coulomb’s law was used. Authors analyzed all factors affecting the incurrence of profits or losses of a retail network.

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Experimental Test of Coulomb's Law

Physical Review D ◽

10.1103/physrevd.2.483 ◽

1970 ◽

Vol 2 (3) ◽

pp. 483-487 ◽

Cited By ~ 22

Author(s):

D. F. Bartlett ◽

P. E. Goldhagen ◽

E. A. Phillips

Keyword(s):

Experimental Test ◽

Coulomb’S Law ◽

Coulomb's Law

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The Stability of Mars’s Annular Polar Vortex

Journal of the Atmospheric Sciences ◽

10.1175/jas-d-16-0293.1 ◽

2017 ◽

Vol 74 (5) ◽

pp. 1533-1547 ◽

Cited By ~ 10

Author(s):

William J. M. Seviour ◽

Darryn W. Waugh ◽

Richard K. Scott

Keyword(s):

Relaxation Time ◽

Time Scales ◽

Time Scale ◽

Thermal Relaxation ◽

Polar Vortex ◽

Radiative Relaxation ◽

Equilibrium Profile ◽

Rotating Shallow Water ◽

The Stability ◽

Topographic Forcing

Abstract The Martian polar atmosphere is known to have a persistent local minimum in potential vorticity (PV) near the winter pole, with a region of high PV encircling it. This finding is surprising, since an isolated band of PV is barotropically unstable, a result going back to Rayleigh. Here the stability of a Mars-like annular vortex is investigated using numerical integrations of the rotating shallow-water equations. The mode of instability and its growth rate is shown to depend upon the latitude and width of the annulus. By introducing thermal relaxation toward an annular equilibrium profile with a time scale similar to that of the instability, a persistent annular vortex with similar characteristics as that observed in the Martian atmosphere can be simulated. This time scale, typically 0.5–2 sols, is similar to radiative relaxation time scales for Mars’s polar atmosphere. The persistence of an annular vortex is also shown to be robust to topographic forcing, as long as it is below a certain amplitude. It is therefore proposed that the persistence of this barotropically unstable annular vortex is permitted owing to the combination of short radiative relaxation time scales and relatively weak topographic forcing in the Martian polar atmosphere.

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