scholarly journals On the electrostatic equilibrium of charges and cavities in a conductor

2016 ◽  
Vol 37 (6) ◽  
pp. 065203
Author(s):  
Aritro Pathak
Keyword(s):  
Electrostatic Equilibrium

The electrostatics of conductors

2018 ◽  
Author(s):  
J. Pierrus
Keyword(s):  
Harmonic Functions ◽  
Conformal Transformation ◽  
Early Stage ◽  
Fourier Method ◽  
Relaxation Method ◽  
Numerical Calculations ◽  
Laplace’S Equation ◽  
Laplace's Equation ◽  
Electrostatic Equilibrium

This chapter begins by proving some important properties of (i) conductors in electrostatic equilibrium, and (ii) harmonic functions. These results underpin most of the remaining questions of Chapter 3. The coefficients of capacitance for an arbitrary arrangement of conductors are introduced at an early stage, and numerical calculations then follow in a number of subsequent questions. Some important techniques (both analytical and numerical) for finding solutions to Laplace’s equation are considered. These include: the Fourier method, the relaxation method, themethod of images and the method of conformal transformation. All of these are discussed in some detail, and with appropriate examples.

The Role of Inertia and Dissipation in the Dynamics of the Director for a Nematic Liquid Crystal Coupled with an Electric Field

2015 ◽  
Vol 18 (1) ◽  
pp. 147-166 ◽  
Author(s):  
Peder Aursand ◽  
Johanna Ridder
Keyword(s):  
Liquid Crystal ◽  
Electric Field ◽  
Nematic Liquid Crystal ◽  
Relative Strength ◽  
Inertial Forces ◽  
Director Field ◽  
Voltage Difference ◽  
Electrostatic Equilibrium ◽  
Variational Wave

AbstractWe consider the dynamics of the director in a nematic liquid crystal when under the influence of an applied electric field. Using an energy variational approach we derive a dynamic model for the director including both dissipative and inertial forces.A numerical scheme for the model is proposed by extending a scheme for a related variational wave equation. Numerical experiments are performed studying the realignment of the director field when applying a voltage difference over the liquid crystal cell. In particular, we study how the relative strength of dissipative versus inertial forces influence the time scales of the transition between the initial configuration and the electrostatic equilibrium state.

The Arc-Length Method from Controlling Load to Controlling Electric Potential

2010 ◽  
Vol 33 ◽  
pp. 636-641
Author(s):  
Xiao Bin Yang
Keyword(s):  
Electrostatic Field ◽  
Electric Potential ◽  
Critical Voltage ◽  
Equilibrium Path ◽  
Nonlinear Coupling ◽  
Arc Length ◽  
Governing Equations ◽  
Coupling Equation ◽  
Plate Electrode ◽  
Electrostatic Equilibrium

This paper generalizes the arc-length method, and proposes a new scheme of controlling equilibrium path including static equilibrium and electrostatic equilibrium. To take example for the thin plate electrode posing on the electrostatic field force, whose governing equations are the two fold nonlinear coupling equation, the method to compute the incremental factor is give in detain. The result is to show that not only the approximate critical voltage is obtained but also the trace after losing stability is found stably.

The thermodynamics of the Vlasov equilibria

1985 ◽  
Vol 33 (3) ◽  
pp. 359-367 ◽  
Author(s):  
E. Minardi
Keyword(s):  
Stability Analysis ◽  
Charge Distribution ◽  
Bifurcation Theory ◽  
Statistical Procedure ◽  
Coarse Grained ◽  
Marginal Stability ◽  
Principle Of Maximum Entropy ◽  
Entropy Functional ◽  
Principle Of Maximum ◽  
Electrostatic Equilibrium

A statistical procedure is applied for constructing an entropy functional associated with a collective Vlasov equilibrium described by a given coarse-grained current and charge distribution. The functional is not at a maximum if the magnetic or electrostatic equilibrium is not unique. This property connects the principle of maximum entropy with bifurcation theory and marginal stability analysis.

Electrostatic equilibrium of a modulated electron beam in a plasma

1984 ◽  
Vol 27 (8) ◽  
pp. 735-739 ◽  
Author(s):  
V. G. Dorofeenko ◽  
V. B. Krasovitskii
Keyword(s):  
Electron Beam ◽  
Electrostatic Equilibrium

Équilibre électrostatique de deux conducteurs sphériques concentriques dont l'un est muni d'une ouverture circulaire

1988 ◽  
Vol 66 (7) ◽  
pp. 559-563 ◽  
Author(s):  
Elie Boridy
Keyword(s):  
Laplace Equation ◽  
Circular Aperture ◽  
Spherical Shells ◽  
Effective Capacitance ◽  
Electrostatic Equilibrium

The Laplace equation for two electrostatic configurations is solved using the method of serial dual equations. These configurations consist of two concentric conducting spherical shells with a circular aperture in one of them. The equations of electrostatic equilibrium are obtained as well as the capacitances, the coefficients of influence, and the effective capacitance. The variation of effective capacitance with the size of the aperture is also discussed.[Journal translation]

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