scholarly journals Exact Partition Function for the Random Walk of an Electrostatic Field

2017 ◽  
Vol 2017 ◽  
pp. 1-5 ◽  
Author(s):  
Gabriel González
Keyword(s):  
Random Walk ◽  
Partition Function ◽  
Charge Distribution ◽  
Electrostatic Field ◽  
Electrostatic Energy ◽  
Dyck Paths

The partition function for the random walk of an electrostatic field produced by several static parallel infinite charged planes in which the charge distribution could be either ±σ is obtained. We find the electrostatic energy of the system and show that it can be analyzed through generalized Dyck paths. The relation between the electrostatic field and generalized Dyck paths allows us to sum overall possible electrostatic field configurations and is used for obtaining the partition function of the system. We illustrate our results with one example.

The Energy of the Electrostatic Field

2020 ◽  
Vol 67 (1) ◽  
pp. 35-41
Author(s):  
Igor’ P. Popov
Keyword(s):  
Electrostatic Field ◽  
Energy System ◽  
Electrostatic Energy ◽  
Research Purpose ◽  
Target System ◽  
Mathematical Form ◽  
Stored Energy ◽  
Energy Materials ◽  
Modeling And Analysis ◽  
Maximum Work

The work is actual due to the increased role of electrostatic energy in connection with the beginning of mass production of ionistors used in the power supply system of electric vehicles, and the need for the development of theoretical support. (Research purpose) The research purpose is in increasing the correctness of electrostatic calculations that exclude the possibility of obtaining unreliable results in the form of infinite electrostatic energy. (Materials and methods) Authors have used methods of mathematical modeling and analysis, studied the mathematical model as the equivalent of an object that reflects in mathematical form its most important properties, such as the laws that it obeys, and the relationships inherent in its constituent parts. (Results and discussion) Authors have studied the electrostatic field created by a system of two charges of the same name or different names. The article presents calculations for charges located in bodies that have the shape of balls. It was found that the results could be generalized to any form of charged objects. They gave three definitions: first, the total stored energy is the energy of the system or object, equal to the maximum work that the system or object can do if it is given such an opportunity. Second, the conditional realized stored energy is a part of the total stored energy of the system or object, equal to the work that the system or object can produce, limited by a condition that excludes the possibility of the system or object performing the maximum work that the system or object can hypothetically perform. The third is a conditional impossible reserved energy as a part of a complete stored energy system or an object that is equal to the work system or object can do and limited by the condition, which excludes the possibility of making a system or object maximum work that target system or object could hypothetically do. Five theorems were proved. (Conclusions) It was found that the main drawback of the actual potential energy formula is an infinitely large increase in energy at radius tending to 0. The obtained formulas for stored electrostatic energy are devoid of this drawback.

scholarly journals On the electrostatic energy of two point charges

2014 ◽  
Vol 36 (3) ◽  
Author(s):  
A.C. Tort
Keyword(s):  
Fixed Point ◽  
Energy Density ◽  
Electrostatic Field ◽  
Electrostatic Energy ◽  
Field Energy ◽  
Field Energy Density ◽  
Physical Features

The electrostatic field energy due to two fixed point-like charges shows some peculiar features concerning the distribution in space of the field energy density of the system. Here we discuss the evaluation of the field energy and the mathematical details that lead to those peculiar and non-intuitive physical features.

Spherical tensor approach to multipole expansions. I. Electrostatic interactions

1976 ◽  
Vol 54 (5) ◽  
pp. 505-512 ◽  
Author(s):  
C. G. Gray
Keyword(s):  
External Field ◽  
Interaction Energy ◽  
Charge Distribution ◽  
Electrostatic Interaction ◽  
Electrostatic Field ◽  
Spherical Harmonic ◽  
Electrostatic Interactions ◽  
Tensor Method ◽  
Multipole Expansions ◽  
A Charge

Using spherical harmonic expansions, the electrostatic field due to a given charge distribution, the interaction energy of a charge distribution with a given external field, and the electrostatic interaction energy of two charge distributions are decomposed into multipolar components. Extensive use is made of symmetry arguments. Comparisons with the Cartesian tensor method are also given.

scholarly journals A Mass-Energy Equivalence Law as E = ½ Mc2

2018 ◽  
Vol 1 (3) ◽  
Keyword(s):  
Charged Particle ◽  
Kinetic Energy ◽  
Electric Field ◽  
Electrostatic Field ◽  
Angular Displacement ◽  
Electrostatic Energy ◽  
Mass Energy ◽  
Energy Equivalence ◽  
Electrical Effect ◽  
The Difference

This paper assumes that the mass and charge of a particle are independent of its speed relative to an observer. A particle of mass m and charge Q moving with its electrostatic field Eo at an angle 𝜽 to the direction of speed v, is considered. The intrinsic energy of the particle is contained in its electrostatic field Eo . The magnetic field, generated by a moving charged particle, does not contain any energy. It is shown that, as a result of aberration of electric field, Eo becomes a dynamic electric field Ev , displaced by aberration angle α from the stationary position. This angular displacement is a distortion which increases the energy of the particle by an amount equal to the kinetic energy. The difference between the energies of dynamic field Ev and electrostatic field Eo , gives the kinetic energy ½ mv2 of the particle, thereby offering a mass-energy law as E = ½ mc2 . It is also shown that a charged particle moving at time t, with acceleration dv/dt, produces a reactive electric field Ea = -μo ɛo QU(dv/dt), where μo is the permeability and ɛo the permittivity of space and φ the potential at a point due to the charge. It is proposed that Ea acts on the same charge Q, to create a reactive force QEa = -μo ɛo QU(dv/dt) = -2Eμo εo (dv/dt) = -m(dv/dt), where the charge Q is in its own potential U, E = QU/2 = ½ mc2 is the electrostatic energy and c2 = 1/μo ɛo, c being the speed of light. The force QEa = -m(dv/dt explains the inertia of a body as an electrical effect caused by acceleration.

Estimate of Coulomb Energies in the Nonlinear Theory of Magnetic Multilayers

1997 ◽  
Vol 11 (16n17) ◽  
pp. 703-706
Author(s):  
W. Baltensperger ◽  
J. S. Helman
Keyword(s):  
Charge Distribution ◽  
Spin Polarization ◽  
Nonlinear Theory ◽  
Electron Gas ◽  
Magnetic Multilayers ◽  
Electrostatic Energy ◽  
Degenerate Semiconductors ◽  
Unit Surface ◽  
A Charge ◽  
Coulomb Energies

A magnetic plane, exchange coupled to an electron gas, generates a spin polarization and in the nonlinear theory also a charge distribution. The corresponding electrostatic energy per unit surface is evaluated. For an electron gas at metallic densities this turns out to be negligible, while it must be taken into account in dilute degenerate semiconductors.

Point charge approximations to a spherical charge distribution: A random walk to high symmetry

1990 ◽  
Vol 67 (12) ◽  
pp. 995 ◽  
Author(s):  
Jeffrey B. Weinrach ◽  
Kay L. Carter ◽  
Dennis W. Bennett ◽  
H. Keith McDowell
Keyword(s):  
Random Walk ◽  
Charge Distribution ◽  
Point Charge ◽  
High Symmetry ◽  
Spherical Charge
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