What is the most ``non-point'' gravitating or electrically charged object?

Abstract

In this paper we search the shape of an aspherical body and the direction in space, for which the greatest deviations from the point mass field (the difference from the inverse-square law) take place for large distances from the field source. It turns out to be a system of two equal point-like masses at the poles of a fixed sphere (giving the greatest positive deviations from the point mass field) and uniform distribution of point-like masses (discrete or continuous) around the sphere equator (giving the greatest negative deviations from the point mass field). In these cases the extremal direction of the field measurement respectively passes through point-like particles and coincides with the axis of symmetry of a ring, which is perpendicular to its plane. Our numerical estimations show that any body can be considered with reasonable accuracy (the relative error in the determination of the field strength is less than $5 \%$) as point-like mass if the distance to the observation point is more than an order of magnitude larger than its characteristic sizes. The problem considered in this paper can help readers to probe the limits of applicability of the field point source model.

On the applicability limits of a model of the magnetic field of a long straight wire

“…It is interesting to compare this result with those obtained in reference [11] for gravitating or electrically charged objects with an aspherical shape. In both cases, we deal with a multiple expansion of field.…”

“…Here, the proportionality coefficient is the value of Q. In the case of the magnetic vector potential, the expression for Q contains the multiplier factor 2 (see equation ( 8)), whereas in the case of scalar potential, this factor is equal to 3 [11]. This means that, at fixed characteristic size and configuration of a system, deviations from the point particle field model may occur at somewhat larger distances than the deviations from the infinite straight wire model.…”

Про Межі Застосування Закону Кулона

“…Заряди мають бути нерухомими відносно системи відліку, в якій розглядається їх взаємодія. У роботі (Ivchenko, 2020) . З виразу (1) слідує, що при…”