两块带电导体的相互作用能

导出了两块导体在给定电量，给定电势时和一块给定电量，另一块给定电势时，3种情况下的相互作用能公式，并从电磁场能量和导体有量两个角度来表示互作用能公式，指出带电导体之间的互作用能一般由电势能，导体带电状态改变做功和外电源提供的能量这3部分构成。     

带电导体系的电场能量

为清晰、透彻地理解静电学中涉及的各种能量的基本概念,本文从场的观点和电荷的观点分析讨论了该问题,并选择了几个熟悉的例子来说明本文认识的合理性.依照场的观点,真空中两个体积足够小的电荷的静电场能量密度为:1/2ε0E21+1/2ε0E22+ε0E1·E2.其中,1/2ε0E21和1/2ε0E22分别为两个电荷单独存在时的电场能量密度,而交叉项ε0E1·E2则为两个电荷电场的相互作用能量密度;它们的空间积分分别为两个电荷单独存在时的静电场能量和两个电荷电场之间的相互作用能量.而从电荷观点出发,此3个静电场的能量分别为两个电荷的固有能和彼此之间的静电相互作用势能.推广到有限体积的孤立带电导体以及带电导体系的情形,可知孤立带电导体的固有能就是其上所有无限小电荷元间的相互作用势能之和,而带电导体系的电场能也就是体系所包含的所有电荷元间的相互作用势能的总和.     

聚吡咯带电态几何结构特征

采用半经验Austin Model 1(AM1)方法,计算了齐分子吡咯聚合物的中性态和带电态的几何结构性质.与中性态相比,带电态下其分子结构表现在C-C键长发生显著改变,单电荷掺杂导致极化子元激发;双电荷掺杂一般情况下产生双极化子,但是在特殊情况下会产生两个分立的单极化子.掺杂4个电荷时,会在聚合物链中产生两个分立的双极化子.     

静电学中的固有能、相互作用能及有关问题

本文用场能的观点定义了电荷系统的固有能与电荷系统间的相互作用能，进而讨论了中性导体静电感应与线性介质极化中的能量问题，明确了两种运用功能原理求相互作用的作法与区别．     

电解液中带电平板与带电胶体球之间的有效相互作用

用Poisson-Boltzmann方程，计算了在具有单价离子的电解质溶液中均匀地带同号电荷的两无限大平行平板间的有效相互作用，以及用Derjaguin近似研究了边界对带电胶体球的影响.不考虑微离子相互作用时，两带电平板只有排斥作用，而且边界条件(面电荷密度)的改变对它们之间的有效相互作用影响不大.带电平板与带电胶体球之间的相互作用也有类似规律. 关键词： Poisson-Boltzmann方程 Derjaguin近似 双电层 渗透压     

走向统一的自然力

所谓"自然力",就是主宰宇宙间物质运动的四种基本相互作用,即作用在一切物体(包括星体)之间的引力;作用在带电(磁)物体之间的电磁力;以及作用在微观粒子之间的强力和弱力。表1给出了这四种自然力的主要特性。     

均匀带电椭球的静电自能——“‘带电厚椭球壳空腔内的电场’一文的补充”续

计算一般形状的均匀带电椭球的静电自能,该椭球是由非导体构成的.方法是把该椭球分割成无限多个与其共轴的、等偏心率的薄椭球壳,通过考虑各个薄椭球壳的自能和它们之间的相互作用能,导出均匀带电椭球的静电自能公式.     

用折合质量巧解弹簧双振子问题

对于两个相互作用物体的相对运动,若合外力为零,则相当于其中一个等效质量为m’=mM/m＋M的物体与一个固定不动的物体在原相互作用力作用下的运动,把等效质量m’称为折合质量．当利用折合质量应用有关公式解题时,只有原相互作用力和时间不随参考系而改变,其余的位移、     

妙用动量定理 巧解系统难题

动量定理的研究对象是单个物体，在求解两个以上相互作用物体组(系统)问题的过程中，若能转换角度，从整体思维出发，巧妙地将相互作用的系统视为单个物体的话，动量定理也是适用的，这时系统所受外力的冲量之和等于系统内各物体总动量的变化量．该方法能使问题化繁为简，化难为易．     

两个带电导体球问题的近似解法

美国大学研究生考题中常有关于带电导体球问题,如:求半径为a相距d的两个带电导体球间电容、相互作用能或作用力;或带电导体球与接地导体平板间电容或作用力;求二球形电极间电阻等。这类问题可以有很多变化,但解法相同。 例1:两半径为a相距d的带等量异号电荷的导体小球,d>>a,求其电容、相互作用能和作用力(准确到　的一次幂)。 分析:由于要准确到　的一次幂,两球间距不能视为无限大。如图1,设球A带正电,球B带负电,由于d>>a,作为零级近似,忽略两球间的静电感应。球外电位可简单地用位于A球球心点电荷q和位于B球球心的点电荷-q激发的电位迭加…     

Electrostatic interaction between two conducting spheres

In the paper we consider the problem of the electrostatic interaction between two charged conducting spheres with arbitrary electrical charges and radiuses. Using the image charges method we determine exact analytical formulas for the force F and for the potential energy W of the interaction between these two spheres as well as for the potential V of the electromagnetic field in an arbitrary point created by them. Our formulas lead to Coulomb’s law for point charges.We theoretically prove the experimentally shown fact that two spheres with the same type (positive or negative) of charges can also attract each other.     

Proximity forces

We have generalized a theorem according to which the force between two gently curved objects in close proximity is proportional to the interaction potential per unit area between two flat surfaces made of the same material, the constant of proportionality being a measure of the mean curvature of the two objects. This theorem leads to a formula for the interaction pontential between curved objects (e.g., two smooth cylinders of mica or two atomic nuclei) which is a product of a simple geometrical factor and a universal function of separation, characteristic of the material of which the objects are made, and intimately related to the surface energy coefficient. We have calculated and tabulated this universal function for nuclear surfaces, using the nuclear Thomas-Fermi approximation. The results can be expressed by a simple cubic-exponential formula which gives the potential between any two nuclei in the separation degree of freedom. Even simpler expressions are found for the interaction energy associated with the “crevice” or neck in the nuclear configuration that would be expected immediately after contact of two nuclei. These “proximity energies” are used to supplement the usual expansion of the energy of a thin-skinned system into volume, surface, curvature, and higher-order terms. The resulting elementary formulas are tested against explicit models of interacting nuclei and against elastic scattering data, and are found to be useful for even quite small mass numbers.     

Prompt efficiency of energy harvesting by magnetic coupling of an improved bi-stable system

In order to improve the transform efficiency of bi-stable energy harvester(BEH),this paper proposes an advanced bi-stable energy harvester(ABEH),which is composed of two bi-stable beams coupling through their magnets.Theoretical analyzes and simulations for the ABEH are carried out.First,the mathematical model is established and its dynamical equations are derived.The formulas of magnetic force in two directions are given.The potential energy barrier of ABEH is reduced and the snap-through is liable to occur between potential wells.To demonstrate the ABEH's advantage in harvesting energy,comparisons between the ABEH and the BEH are carried out for both harmonic and stochastic excitations.Our results reveal that the ABEH's inter-well response can be elicited by a low-frequency excitation and the harvester can attain frequent jumping between potential wells at fairly weak random excitations.Thus,it can generate a higher output power.The present findings prove that the ABEH is preferable in harvesting energy and can be optimally designed such that it attains the best harvesting performance.     

Most probable and average energy losses of the beam of monoenergetic charge particles with average and low energies at multiple scattering

The results of statistical modeling of the discrete process of multiple inelastic scattering are presented. This process is modeled to find the most probable and average energy losses of a beam of charged particles (electrons and protons) passing through a material layer with a given thickness. The proposed approach is based on determining the most probable energy loss at single small-angle scattering, on including the effect of the statistical probability on this quantity at multiple scattering, and on determining the average number of inelastic interactions for particles in a film with a known thickness. The dependence of the particle energy lost during interaction with atomic electrons on their relative motion is taken into account for low-energy particles. A new interpretation is offered for the parameter J in the logarithmic term in the formulas for the average and most probable energy losses of charged particles. A computational scheme for this parameter as an average potential energy of atomic electrons is given.     

二维环状无限深势阱中的朗道能级

对于带电粒子在磁场中的运动,在各种教科书上都有详细的阐述,但是对于限制在二维无限深势阱的带电粒子,现在流行的各种量子力学教科书上都没有阐述.本文主要讨论二维无限深势阱中的能级和朗道能级.     

弹性势能的表达式的实验验证

教材上从理论上探究了弹性势能的表达式,结合该探究过程,利用弹性势能与重力势能和动能的转换关系设计了2个验证性实验.     

强流柱对称相对论电子束的势能与发射度

推导了柱对称相对论电子束在漂移管内的空间电荷势及相互作用势能,分析了势能在束流传输过程中的变化规律,并与束流均方根发射度的变化方程比较。指出一部分势能随束流传输过程中包络振荡而呈现出可逆的变化;而另一部分势能则在束流传输系统及束流本身非线性力的作用下,随着电荷密度分布变化而转为电荷横向热运动能量,从而导致束流归一化发射度的增长,这种转化是一个不可逆的过程。     

Electrostatic interaction between a rod-like macromolecule and a circular orifice/disk in an electrolyte solution

We present the solutions of the interaction energy for a colloid system with a charged rod-like macromolecule immersed in a bulk electrolyte and moving along the axis of a circular orifice or disk (orifice/disk).The calculation requires a numerical computation of the surface charge profiles,which result from a constant surface potential on the macromolecule and the orifice/disk.In the calculation,remarkable divergences of the surface charge emerge on the edges of the macromolecule and the orifice/disk,which are well-known edge effects.The anisotropic distribution of the surface charge (effective dipole) results in an attraction between these two charged objects.This attraction is enhanced with the increase of the screening length of the system for both the orifice and the disk systems.However,the sizes of the orifice and the disk reduce to different effects on the interaction energy.     

层间作用对HgS/CdS/HgS柱状纳米系统电子能量的影响

确立了柱状纳米系统电子势能随距离的变化关系，以HgS/CdS/HgS柱状纳米系统为例，讨论了层间作用对电子能谱的影响.结果表明：电子能量随势垒宽度和波矢的增大而增大，随势阱宽度的增大而减小；层间互作用会增大电子能量，但不会改变电子能量随势阱和势垒以及波矢的变化趋势. 关键词： 层间作用势 HgS/CdS/HgS柱状纳米系统 电子能量