点电荷与介质球系统电势的计算和讨论

计算了点电荷与介质球系统的电势．指出点电荷与导体球、点电荷与无限大导体平面或介质分界平面均匀外电场中有导体球或介质球系统的电势都可由点电荷与介质球系统的电势给出。     

基于等效原理求解介质球极化场问题

文章利用场的叠加原理和连带勒让德多项式的性质,并结合等效偶极矩模型导出导体球在均匀电场中感应场的表达式。以此为基础,基于电磁场的等效原理分析了介质球和介质球壳在均匀电场中的极化场问题。计算结果与相关文献相一致,从而证明了该方法的正确性。最后探讨了时谐电磁场对介质球的极化可以用电偶极矩场近似的条件,并阐明介质球的极化场在电磁辐射与散射、纳米球颗粒共振及电磁隐身中的作用。对于更好地理解极化的物理本源以及应用具有指导意义。     

电荷投影法在研究无限长导体薄板电荷分布规律中的应用

利用无限长均匀带电圆柱面的电荷分布规律和无限长带电直线的场强公式,采用电荷投影法推导了有限宽无限长带电导体的面电荷分布规律.根据电势叠加原理推导了电势积分式,利用场强与电势之间的关系推导了电场强度两个分量的积分式.将公式无量纲化,通过数值积分计算了电势和场强的分量之值.通过作图,显示了有限宽无限长带电导体薄板的电势和场强,画出了二维等势线和电场线,充分显示了场强的分布规律.     

共形映射法求无限长带电直导线的电势

沿着主轴放置的无限长均匀带电直导线在有三个两两正交主轴方向的各向异性电介质中激发的电场是二维静电场。由无限长均匀带电直导线在各向异性电介质中的电势表达式,以平面镜像法为统一模型,应用共形映射,可求解出当存在一类接地导体的边界较为复杂时其所激发的电势。     

无限长直椭圆柱(或柱壳)形带电导体外的电场分布

利用保角变换,将无限长导体椭圆柱面变为无限长导体圆柱面,求出无限长导体椭圆柱面外的电势分布并进而给出电场分布.     

带电细圆环与导体球壳系统的场分布

先依电象法,推导均匀带电圆环在金属导体球壳内的"象电荷";再在球坐标系下,根据电场强度的计算公式与Tay-lor展开式,计算出均匀带电细圆环在全空间的电场分布的级数形式解;进而结合唯一性定理和电场的叠加原理,获得带电细圆环与导体球壳系统的空间场分布.     

金属目标表面气体放电单元放电过程的PIC-MCC模拟

 对目标表面的浮地导体边界的存在及其对单元气体放电过程所产生的影响进行了研究，针对导体边界条件，应用高斯定理和电荷守恒定律推导出这种边界条件的数值处理方法，得到了有界等离子体空间电势的数值分布。电场的数值计算表明，浮地导体的电势随着内部场的变化而变化，其大小介于两个电极的电势之间，对放电区域的电场分布产生较大的影响。 对金属目标表面放电单元的放电过程的PIC-MCC模拟结果表明， 浮地导体的存在能够改变放电空间的电场结构，形成不均匀场，有利于气体的电离和等离子体区域的形成，同时将使虚阳极所形成的电势平台在边界附近下陷，导致等离子体壳层的厚度变小。     

圆形区域变化磁场激发 涡旋电场的问题剖析及案例分析

剖析涡旋电场的分布以及涡旋电场中非导体约束和导体约束条件下的电势问题, 给出在限定的圆形区 域内均匀变化磁场中的涡旋电场、 感生电动势与电势的分布规律, 以及在这限定的圆形区域内均匀变化的磁场中, 非导体约束和导体约束条件下电势的计算与比较. 通过在涡旋电场中对电源、 电势及电压等概念的引入,澄清了一 些在大学物理教学中涉及涡旋电场的容易模糊、 难于理解的概念. 对涡旋电场的一个具体案例进行了详细分析     

无限长均匀带电线与非接地带电圆柱导体系统的等势线与电场线方程

利用电像法和解析函数的规律,得出无限长均匀带电线与非接地带电圆柱导体系统的电势和电场强度表达式,并给出了等势线与电场线方程,且讨论了同性带电体之间的吸引力.     

关于静电屏蔽上限的讨论

将导体壳放入外电场中,导体会在表面产生感应电荷,并达到静电平衡状态,导体壳腔内的电场处处为零,这就是静电屏蔽效应.然而,如果外电场极强,或者导体内部的自由电荷太少,以至于感应电场不能完全抵消外电场,则静电屏蔽效应将失效,这就是静电屏蔽的上限问题.本文从静电屏蔽的原理出发,将导体壳简化为一对平行金属平板的模型,定量的讨论了这一问题.通过计算我们发现,由于金属内存在大量的自由电子,在非极端问题中,宏观的导体装置都远远不会遇到静电屏蔽的上限问题.     

线电流与无限长磁介质圆柱系统的磁矢势的计算及讨论

用镜象电流法和分离变量法计算了线电流与无限长磁介质圆柱系统的磁矢势,指出线电流与无限大磁介质分界平面、线电流与超导体圆柱、均匀外磁场中有磁介质圆柱系统时的磁矢势都可以由线电流与磁介质圆柱系统的磁矢势的极限情形给出.     

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.     

Controlling electric field distribution by graded spherical core-shell metamaterials

This paper investigates analytically the electric field distribution of graded spherical core-shell metamaterials, whose permittivity is given by the graded Drude model. Under the illumination of a uniform incident optical field, the obtained results show that the electrical field distribution in the shell region is controllable and the electric field peak’s position inside the spherical shell can be confined in a desired position by varying the frequency of the optical field as well as the parameters of the graded dielectric profiles. It has also offered an intuitive explanation for controlling the local electric field by graded metamaterials.     

导体壳内外的电场彼此独立的简易证明

本文提供了一种证明导体壳的内外电场彼此独立的简易方法.     

由接地导体限定的无限深槽内线电荷的电场

利用复数坐标系z上的施瓦茨-克利斯多菲变换和镜像法,计算由接地导体限定的无限深槽内线电荷电场中的电势分布和场强分布,给出电场线与等势线方程,并利用数学软件Matlab绘制出其电势分布三维图、电场线和等势线(面)图.     

Electric field simulation and measurement of a pulse line ion accelerator

An oil dielectric helical pulse line to demonstrate the principles of a Pulse Line Ion Accelerator (PLIA) has been designed and fabricated. The simulation of the axial electric field of an accelerator with CST code has been completed and the simulation results show complete agreement with the theoretical calculations. To fully understand the real value of the electric field excited from the helical line in PLIA, an optical electric integrated electric field measurement system was adopted. The measurement result shows that the real magnitude of axial electric field is smaller than that calculated, probably due to the actual pitch of the resister column which is much less than that of helix.     

电偶极子位于均匀介质球中时球外电场的研究

采用分离变量法求解了电偶极子位于均匀介质球中时复连通域的拉普拉斯方程和泊松方程,求出了球内外两种不同介质的电势分布和球面上的极化电荷分布;通过求解二阶非线性微分方程得到了球外的电场线函数;利用计算软件Math-ematica 5.0,作出了相应的相互正交的等势线簇图形和电场线簇图形,并且进行了必要的讨论.     

用电介质镜像法计算线电荷与介质圆柱所形成的电场

利用电介质镜像法计算线电荷与介质圆柱体所形成的电场,给出电势与场强的解析表达式,进一步得出等势线与电场线方程,并利用软件MATLAB绘制出电场线和等势线(面)图予以验证.     

Capacitance of an elliptical disk on a semi-infinite dielectric material

Using an integral transform, the mixed boundary value problem of a conducting, elliptical disk on a dielectric half-space in an electric field is reduced to the solution of an integral equation. An analytical expression of the electric system capacitance is derived, which is a function of the eccentricity of the elliptical disk. The electric charge and electric stress distribute non-uniformly over the surface of the elliptical disk and display local singularities at the edge of the elliptical disk. The square root singularity of the electric field at the edge of the elliptical disk leads to the divergent of the resultant force on the elliptical disk, which is physically unrealistic. There likely exist geometrical constraint and/or field constraint to limit the presence of the square root singularity of the electric field. For any symmetric conductor in an infinite space that consists of air (vacuum) and a semi-infinite dielectric material with symmetric plane being in the interface between the air and the dielectric material, the electric potential in the space is independent of the dielectric constant of the dielectric material.     

Multiple Image Method for the Two Conductor Spheres in a Uniform Electrostatic Field

A method using multiple mirror images of point charges is put forward to analyze the polarization of two identical conductor spheres in a uniform electrostatic field. By use of the method, the electric field distribution and the interaction force between two spheres can be calculated accurately even for very small gap between two spheres. Our results show that the magnitude of the product of the gap between two spheres and the local electric field in the center of the gap is approximately in the same order and the interaction between two spheres increases very fast as the two spheres are close to each other. We also show that the interaction force between two conductor spheres is almost same with that between two dielectric spheres with high permittivity.