介质球在点电荷电场中产生的电势分布规律

推证了介质球在点电荷电场中产生的电势分布规律;同时由此推出了当介质球的电容率ε→∞时,介质球在点电荷的电场中为等电势体,以及金属导体球在点电荷电场中产生的电势分布规律．     

点电荷与导体球系统的电场线

用电像法将点电荷与中性导体球系统的电场化为一维点电荷分布系统的电场,导出电场线满足的方程,利用Mathematica软件画出了电场线簇图形,并对点电荷与接地导体球、点电荷与带电导体球两系统的电场线进行了描绘。     

粗糙导体表面的镜象问题

由泊松方程和边值条件，解析地讨论粗糙导体表面的镜象问题，计算结果表明：当点电荷和观察点的位置离导体平面较近时，表面粗糙度对电势的影响和表面粗糙的平方平均值成正比，与离导体表面的距离的三次方成反比。     

点电荷在三层介质中势的物理解释与光学类比

导出点电荷三层介质中的电势，并给出了物理解释，利用光学类比处理镜像问题，直观地给出多怪平面介质中镜像电荷的位置和大小。     

格林互易定理

格林互易定理在研究静电场的互易性和解决某些静电场问题时是很有用处的.它的内容很简明:在线性介质中,设有一个静电独立的[1]n 1导体系统,0号导体为参考导体,!号(i=1,2,…,n)导体所带电荷为Qi,电势为vi;此同一导体系统的另一种带电方式如果是i号(i=1,2,…,n)导体所带电荷为Qi,电势为Vi,则在这两种带电方式的电荷与电势之间必有关系式存在。它的证明方法比较多,有的从导体系统的两种带电状态的能量之差只与这两种带电状态本身有关,而与由一种带电状态如何过渡到另一种带电状态的具体方式无关进行证明[1],也有的是先证明它对点电荷系统成立…     

外场中介质球周围电势分布的一种新解法

利用点电荷与介质球系统的镜像电荷分布规律以及对外加电场源的等效,并结合场的叠加原理和连带勒让德函数的性质导出在外加电场中介质球周围电势分布的表达式。在此基础上,讨论了几种特殊情形,从而验证了其正确性。本文方法新颖,对于更好地理解球形介质边界的镜像、场的等效原理以及特殊函数在静电势的求解中的应用具有指导意义。     

“电磁学”教学问题两则

1.不接地导体壳内的电荷改变位置不影响壳外电场分布的问题。 在电磁学讨论静电屏蔽时,常出现这样的问题:如图1所示,点电荷q在导体壳内移动位置时,壳外的电场分布是否改变见了这问题采用唯一性定理是易于解决的.但在普通物理范围内,如何解决呢;我们以球形导体壳为例加以说明.如图2所示,设导体壳为球形壳,在球心放置一点电荷q,此时球壳上的电势为当q从球心移到a点(离球心为r)时,设球壳上的电势为U’.由于导体是等势体以及球对称性,q在以r为半径的球面上任一处,导体壳上的电势均为U’。设 电荷Q均匀地分布在半径为r的球面上,则带电为Q 的球…     

带电子导体球壳系统的精确解

导出了包围有接了导体球的带电导体球壳与地组成的静电系统的精确解，证明在该系统中，不管球壳与地之间的距离如何，电荷在地面产生的电势与在无限锭产生的电势总是相等，指出不精确解导导致无限远与大地的电势不等的错误结论。     

带电导体球壳系统的精确解

导出了包围有接地导体球的带电导体球壳与地组成的静电系统的精确解．证明在该系统中，不管球壳与地之间的距离如何，电行在地面产生的电势与在无限远产生的电势总是相等．指出不精确解会导致无限远与大地的电势不相等的错误结论．     

用电像法讨论点电荷与导体球间的相互作用

用电像法讨论点电荷与接地导体球、绝缘导体球、一个和电源连接的导体球之间的相互作用.     

Electric field and force on a conducting sphere in contact with a dielectric solid

This paper presents the analysis of electric field and force on a conducting sphere lying on a dielectric solid under a uniform field. To achieve high accuracy, we have applied the analytical method of successively placing three infinite sequences of point and dipole charges (zero- or first-order multipoles). The electric field is highest at the contact point, called the triple junction, where the conductor, the dielectric solid, and the surrounding medium (gas or vacuum) meet together. Both the contact-point field and the force increase with the permittivity ratio of the solid to that of the surrounding medium. The resulting force always attracts the sphere to the solid, in contrast to the repulsive force in the case of a conducting sphere lying on a plane conductor under an external field. We have given very simple formulae for approximating the contact-point field and the force which agree with the precise values within a difference of 3% for permittivity ratios up to 32 and 64, respectively.     

导体球壳上感应电荷及空间电场的分布(2)

本文利用镜象法讨论了在不接地导体球壳附近有点电荷时，空间的电场分布和球壳表面上感应电荷的分布。     

聚焦部分相干涡旋光束作用在介质球上的光阱力(英文)

应用部分相干理论推导了部分相干贝塞尔涡旋光束经过透镜聚焦后的光强分布表达式。在雷利散射范围内,利用光作用在介质球上的梯度力和散射力公式,主要讨论了拓扑荷数、相干长度、参数α以及介质球的大小选择对于梯度力和散射力的影响。数值模拟结果表明,作用在介质球上的梯度力和散射力随着拓扑荷数、相干长度或参数α的增大而减小。当拓扑荷数为0,1时,稳定的3维光阱能被获得,并且能被应用于操控折射率低于周围媒介的粒子。     

Mathematical modeling of a diode system based on a field emitter

A mathematical model of a diode system based on a field emitter is considered. The field emitter is modeled in the following way: the tip is a conducting sphere; the “body” is a solid dielectric with a spindle surface of revolution. The anode is a part of the spherical surface and the substrate of the emitter is a spherical surface or a plane. The influence of a space charge is not taken into account. To find the electrostatic potential distribution, the methods of separation of variables and paired equations are used. The problem of finding unknown coefficients in the eigenfunction expansion of the potential is reduced to the solution of the system of equations, which includes linear algebraic equations and the Fredholm equation of the second kind. Thus, the computational problem of the distribution of electrostatic potential in the entire domain of the investigated system is solved.     

Retarded Van der Waals potential between a conducting plane and a polarizable particle

The method of zero point energy is used to obtain the retarded Van der Waals potential between a perfectly conducting plane and a particle possessing both electric and magnetic polarizability. As a special case, the force between a conducting plane and a conducting sphere is obtained.     

Analysis of general multipolar images on dielectric layers for the calculation of DEP force

An axisymmetric field problem of a sphere and a multi-layered planer dielectric body is investigated based on the multipolar expansion method. First, the multipolar potential, produced by the sphere and expressed in the spherical coordinate system, is re-written in the cylindrical coordinate system as an integral of Bessel function. Then the field problem is solved with the boundary conditions at the planer interface of the dielectrics, and the obtained potential is written back to spherical harmonics, which can be regarded as “image multipoles” inside the dielectric body. The “images” influences back the “multipoles” on the sphere, and the field can be determined by solving these relations in self-consistent manner. DEP force exerted on the particle is calculated as the multipolar interaction, as well as the capacitance for the case involving a conducting sphere and a conducting plane.     

Transition and diffraction radiation from a charge on a perfectly conducting sphere

The problem of transition radiation from a charge on a perfectly conducting sphere and diffraction radiation from a charge flying near the same sphere is solved. The radiation energy, spectrum, and polarization are found. The result is obtained for the limiting case of dipole radiation and the trajectory of the charge passing through the center of the sphere.     

Transition and diffraction radiation from a charge on a radially conducting sphere

The problem of transition radiation from a charge on a radially conducting sphere is solved. The motion of the charge through the center of the sphere is considered for dipole radiation.     

Ellipsoidal harmonics and their application in electrostatics

Ellipsoidal functions and ellipsoidal co-ordinates, naturally adapted to the treatment of potential problems involving ellipsoidal boundaries, are due to a relatively complicated mathematical appearance avoided in the majority of textbooks on electromagnetism, leading to an unjustified ignorance of the whole system. The paper at hand is devoted to showing that the system is worthwhile using and investigating. By first recollecting the key results of the co-ordinate system and the related potential functions, including the indispensable orthogonality result and the reciprocal distance formula, basic potential problems of electrostatics are reviewed. Closed-form expressions are thereupon derived for the induced charge and its centroid in the case of a point charge influencing a grounded ellipsoid. An image source interpretation, generalising the image solution for a sphere, follows easily from these expressions, as well as an approximate expression for the mutual capacitance between two ellipsoids or a parallel disk capacitor. An expression is also given for the total polarisation induced in a dielectric ellipsoid by the influence of a point dipole.     

导体球壳上感应电荷及空间电场的分布(1)

本文利用镜象法讨论了在接地导体球壳附近有点电荷时，空间的电场分布和球壳表面上感应电荷的分布。