几种孤立带电导体的电荷面密度与曲率的关系

引言 本文试图计算某些形状规则的带电导体共电荷面密度与曲率的关系.本文的基本思路是:根据带电导体电场的电势[1],[2],可以求出导体表面的电荷密度(σ=E/4π=｜φ｜/4π).再利用微分几何有关曲率的知识,就可得到电荷密度与曲率的关系式. 下面先介绍微分几何有关曲率的知识.二、主曲率和总曲率[3] 平面曲线的曲率概念我们是熟悉的.下面我们说明曲面的曲率可以通过平面曲线的曲率来表示. 通过曲面上任一点M的法线,可以作出无穷多个平面,每个平面与曲面的交线称为M点的法截线.M点的法截线有无穷多条,每条都是平面曲线,都有确定的曲率.设M点…     

尖端导体面电荷密度的两种不同模型

普通物理学教材以尖端导体放电现象为例说明,曲率越大的地方,面电荷密度也越大,本文用两个不同的物理模型给尖端放电现象以理论解释．     

孤立带电导体的电荷分布

本文就孤立导体面电荷密度与表面的曲率的关系进行定性地分析．带电导体处于静电平衡状态时，导体内部电场强度必定处处等于零，即Ｅ内＝０．由Ｅ内＝０，可以直接导出如下几点推论：（１）导体是等势体，表面是等势面；（２）导体表面场强处处与表面垂直；（３）由高斯定...     

孤立带电导体的面电荷密度和曲率的关系

孤立导体带电时电荷在表面上如何分布是电磁学中一个很有意义的问题.中外的物理教科书都要讲到,表面曲率越大处,电荷密度也越大,但都未能给出一个正确的定量关系,这未免使人感到不足. 笔者对这个问题的研究结果指出,至少对几种表面形状(二次曲面)的导体来说,面电荷密度和表面曲率之间的确存在一个定量关系,这也许有助于我们对此问题的理解.一、表面弯曲程度的量度─—高斯曲率 按照微分几何,曲面在一点的弯曲程度由曲面在该点的高斯曲率表示.设曲面的方程为z=z(x,y),则曲面的高斯曲率为 现分别求出椭球面、双叶旋转双曲面、旋转椭圆抛物面的…     

带电导体椭球的面电荷密度与主曲率半径的关系

求出了带电导体椭球的面电荷密度与主曲率半径的关系.     

等势条件下两带电导体球的电荷分布

本文通过多重镜像法求解了等势条件下两个带电导体球的电荷分布问题,主要关注两球的电荷量以及平均面电荷密度随两球半径和两球间距的关系.通过选择合适的坐标,给出两导体球接触时,n级镜像电荷电量和位置的通式,及总电量的解析表达式.研究发现,当两导体球直接接触时,两球所带的电荷量可以严格求解,并给出了两球的电荷量之比表达式.随着两等势导体球间距的增大,两球所带的电荷量之比趋于半径之比.本文还讨论了一个导体球的半径趋于0的极限情况,小球与大球的电荷量之比趋于0,平均面电荷密度之比在两球不直接接触时趋于无穷大,而在两球直接接触时趋于π²/6.     

几种不同形状导体表面的电荷面密度

对无限大导体表面，楔形导体表面，半圆柱形凸起表面电荷面密度进行了具体的计算，结果表明在静电平衡的条件下导体表面虽曲率相同，但表面电荷面密度却可以不同．     

均匀磁场中旋转的轴对称导体上的电荷分布析

分析了均匀磁场中旋转的轴对称导体上的电荷分布，指出这里不存在普遍的面电荷密度公式。     

孤立带电导体面电荷密度的分布

关于孤立带电导体表面上面电荷密度的分布问题,在普通物理学教科书中都有讨论,一般只是作为实验结论,在理论分析上比较粗略。本文试图从靜电场的基本性质出发,推导出电力线束发散程度与等位面的曲率之间的普遍关系式,从而定性地讨论孤立带电导体表面电荷分布情况。     

导体旋转椭球电学量的一种计算方法

用一种新方法，计算了孤立导体旋转椭球的面电荷密度、电容、电势和电场强度，并得出相应的解析表达式。     

有限长导体棒的电荷分布的数值模拟

利用有限差分法对有限长导体棒电荷面密度进行了数值模拟.数值模拟结果说明,有限长带电导体棒面电荷分布不仅与导体表面的曲率半径有关,还与导体的总体形状以及导体周围环境中其他导体的分布有关.     

Self-consistent field theory of adsorption of flexible polyelectrolytes onto an oppositely charged sphere

The adsorption of flexible polyelectrolyte （PE） with the smeared charge distribution onto an oppositely charged sphere immersed in a PE solution is studied numerically with the continuum self-consistent field theory. The power law scaling relationships between the boundary layer thickness and the surface charge density and the charge fraction of PE chains revealed in the study are in good agreement with the existing analytical result. The curvature effect on the degree of charge compensation of the total amount of charges on the adsorbed PE chains over the surface charges is examined, and a clear understanding of it based on the dependences of the degree of charge compensation on the surface charge density and the charge fraction of PE chains is established.     

Electric field localizations in thin dielectric films with thickness non-uniformities

Thickness non-uniformities in electrostatic capacitors and in electroactive polymers – arising from manufacturing processes or electromechanical induced inhomogeneous deformations – may lead to drastic charge and electric field localizations and, ultimately, to an anticipated device failure. Based on a geometric interpretation of the Gauss equation enlightening the effect of the electrode curvature, we obtain an analytic expression of the electric field and of the surface charge density localization for non perfectly planar capacitors with symmetric thickness non-uniformities. The efficiency of the model is exploited by analyzing specific boundary value problems of technological interest.     

The Coulomb explosion of charged drops

In the framework of the density functional theory using a simple variational model we have calculated the first-order size corrections to electro-physical characteristics of small metal particles. We have discovered that the curvature correction to the surface energy is of positive sign. We have shown that it is possible to use macroscopic electrodynamics in calculations of the ionization potential and the electron affinity. We have determined the maximum charge which can be retained by a particle of a given size.     

Effect of the space charge of emitted electrons on field electron emission

It is shown that the conventional technique of substituting the field strength at the space charge-emitter interface that is calculated with the Poisson equation into the Fowler-Nordheim formula considerably overestimates the effect of space charge on field electron emission. In this work, the space-charge-induced field attenuation as a function of the emission current density and radius of curvature of the emitter surface is derived using the model of a planar space-charge layer. It is argued that field electron emission cannot be studied in terms of the spherical diode model, since it assumes the presence of a space charge on the back (nonemitting) emitter surface, which is in fact absent. It is stated that one should consider the discrete character of the charges when investigating the space charge in field electron emission, because the mean spacing between the electrons emitted far exceeds the emission barrier width.     

Length-Scale Dependence of Hydration Free Energy: Effect of Solute Charge

Size and curvature are important determinants of particle wettability, in addition to surface chemistry and texture. Hydration free energy of a nonpolar solute scales with volume for small solutes and with surface area for larger ones. If the solute acquires a surface charge, the scaling regimes can be affected, with size-dependence of the charge playing a critical role. For isolated particles grown at fixed surface charge density, the Born approximation gives scaling of hydration free energy with volume. We consider a distinctly different but practically important scenario, where the charged solute and surrounding counterions are dissolved together. For this process, our molecular simulations demonstrate the electrostatic contribution to the solvation free energy, calculated per unit area of the solute, to be virtually independent of solute size. We explain this behavior in terms of counterion shielding effect on the curvature-dependent solute energy in the dehydrated state, an effect closely balanced by the influence of dielectric screening in water. As a result, for moderate surface charge densities of the solute, the net electrostatic contribution is dominated by counterion solvation, and scales with solute surface area independently of the ionic strength in the solution.     

On the relation of the Methagalaxy mass to the gravitation constant. 1. from Einstein’s theory to the Einstein–Cartan theory

The notion of the dimensionless gravitational charge defined through the Planck mass and the fundamental constants specifying this mass itself is introduced. The Big Bang is related to the unified physical interaction decay and the drop of Newton’s gravitational constant by 40.67 orders of magnitude in comparison with the electromagnetic constant taken as unity. This causes an increase in theMetagalaxy curvature radius by the same value and a decrease in the average density of space–time curvature sources by 122 orders of magnitude: from the maximum allowable Planck density to the observed critical density. The microphysics appears naturally related to cosmology.     

非球形水下爆炸气泡坍塌机制

 为研究非球形水下爆炸气泡的坍塌机制和射流特性,采用水下爆炸实验和数值模拟相结合的手段,研究了典型的柱形装药自由场水下爆炸气泡的运动过程。实验结果与数值模拟结果符合较好,通过对比发现,非球形水下爆炸气泡坍塌所形成的射流与球形气泡坍塌射流的行为存在差异。研究结果表明：非球形气泡的坍塌过程与气泡初始形态的局部曲率半径有关,初始气泡表面曲率半径大的区域的初始膨胀速度较曲率半径小的区域的小,坍塌时刻也较早,导致气泡产生非球形坍塌。