两个带同性电荷导体球之间一直保持排斥力的条件

两个带同性电荷导体球之间的相互作用是大学物理教学中的重要问题.已有研究结果表明:在一般情况下两球之间会存在吸引力,但在两球电荷与半径比值相关的特殊条件下,两球之间会一直是排斥力.本文首先通过相互作用的定性讨论,推广了两球之间一直是排斥力的条件,拓展了两球之间一直是排斥力的参数区间.然后利用由系列电象法求出的两导体球的电容系数,用数值计算方法验证了定性分析的结论,发现两个带同性电荷的导体球确实可以在更宽泛的参数条件下一直保持排斥力.     

分层球形导体中任意位置直流电流元产生电位的解析解

建立了任意层球形导体头模型.从泊松方程出发，利用电磁边界条件求解了分层球形导体中由任意位置直流电流元产生电位的一般解析解，并且给出了一种以矩阵形式表示的快速求解电位表达式中相关系数的方法.以表示头皮、颅骨、脑脊液和脑的四层球导体模型为例，对解析解进行了计算.结果表明，此解在除源点外的全域内收敛，且比仅用球谐函数展开形式的电位收敛快，计算量明显降低.给出了等位线图和流线图，表明低电导率对电位分布和电流流向的影响不可忽视.还给出了球表面电位分布特征，这有利于脑电逆问题的研究以及对脑电位测量结果的解释. 关键词： 电位 电流元 分层球形导体 脑电     

像偶极子法计算导体颗粒簇团的偶极矩

计算均匀电场中颗粒簇团的偶极矩通常是困难的,这是因为颗粒间的相互耦合较难处理.这种相互耦合使颗粒的极化依赖于簇团的结构和大小.利用像偶极子法对这种耦合加以分析.首先,分别考虑了置于纵向和横向电场中的任意间距的等径导体球对,确定了各球上的像偶极子和像电荷及其分布.之后,计算了由4个置于正方形顶点和8个置于立方体顶点的导体球构成的簇团的偶极矩,并给出紧凑表达式.与先前的结果进行了比较,获得了很好的一致性. 关键词： 偶极矩 颗粒簇团 像偶极子法 分形     

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.     

确定接地导体球内像电荷的一种原始思路

针对许多参考书中讨论电像法的基于相似三角形的切入思路,但此法思路并不自然,这里给出一种从极其自然的原始思路出发（只用点电荷的电势公式）,确定接地导体球内的像电荷的方法（包括电荷量的大小和位置）,并将接地无限大导体板问题作为本问题的特例处理．     

带电线电场中导体球上的特定电荷分布

研究了带电导体球在带电直线电场中的电荷分布问题,并计算了两种特定情况下导体球表面的电荷密度.     

导体壳问题的静电演示

导体壳问题是静电场中导体的典型问题,讲解时比较抽象。我们给范德格喇夫起电机增加了一点附件,就能演示静电场中的所有导体壳问题,附件制作简便,演示效果明显,很说明问题。一、仪器装置其装置是在一般的范德格喇夫静电起电机的电极球上,罩一个能上下移动的金属球壳,如图1所示。整个球壳由两个半球壳组成(自己试作,可用两个半球铝质灯罩代替)。上半球壳上开有圆孔,以便观察与探取电荷。下半球壳固定在一个有机玻璃筒     

关于两个导体球间的电容问题

本文利用镜像法,计算了两相互接触的带电导体球的电容.接着再用镜像法计算两相距一定距离的具有相同半径的导体球间的电容,且其极限情况与已知结果相同.然后用Matlab对结果进行了数值分析.     

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。     

两种球形接地电极的电阻

本文利用静电比拟法计算了两个半球形接地电极间的电阻及一浅埋接地导体球的接地电阻.     

Investigation of interaction between methanol fed tandem porous spheres burning in a mixed convective environment

Flame interaction during the burning of two porous spheres in tandem arrangement fed with methanol and subjected to a mixed convective environment, has been studied experimentally and numerically. Porous sphere technique is employed for experimentally simulating the burning characteristics of methanol transpired spheres of different sizes, separated by fixed distances. The mass burning rates from both the spheres and visible flame stand-off distances from the sphere surfaces have been measured in the experiments. In the numerical simulations, transient, axisymmetric, mass, momentum, species and energy conservation equations are solved using a finite volume technique based on non-orthogonal semi-collocated grids. Features of the numerical model include finite rate chemistry and temperature and mixture composition dependent thermo-physical properties. Burning of tandem porous spheres in an air stream flowing vertically upwards, at atmospheric pressure has been simulated for different sphere sizes, separation distances and free stream velocities. The numerical predictions have been compared with experimental results. Results reveal that when two spheres burn one over the other, the transition from envelope to wake flame is delayed when compared with that of an isolated sphere. For two spheres of same diameter burning one over the other, depending on the separation distance, flame blows-off after the occurrence of transition from envelope to wake flame in the bottom sphere. For the case of larger sphere at the top, either the flame stabilises in the recirculation zone formed in between the spheres or the flame from the smaller sphere lifts off and stabilises near the front portion of the larger sphere, depending on the separation distance. At higher separation distances, around four times the diameter of the sphere, both the spheres burn independently. The burning rate undergoes complex variations with air stream velocity depending on the sphere sizes and separation distances.     

磁性液体中非磁性小球与磁性纳米颗粒的相互作用及磁组装

利用磁性液体与聚苯乙烯小球溶液混合得到的复合磁性液体, 研究了聚苯乙烯小球和磁性纳米颗粒在外加磁场作用下的动力学过程. 实验结果表明, 当外加磁场的方向平行于样品平面时, 聚苯乙烯小球在沿着磁场的方向上表现出相互吸引而形成链状结构, 其动力学过程可分为聚苯乙烯小球被反磁化产生相互吸引而形成短链的快过程以及短链间相互吸引形成长链的慢过程; 当外加磁场的方向垂直于样品平面时, 相邻聚苯乙烯小球表现出排斥的相互作用而形成短程有序的二维结构, 当磁场强度增加到一定的阈值时, 聚苯乙烯小球和磁性纳米颗粒形成的团簇会产生相互吸引而组装成复合式的花瓣结构. 关键词： 磁性液体 磁组装 非磁性颗粒     

Time-dependent interaction across two conducting spheres in an applied electrostatic field

Charged particles exist widely in variety of technological areas as well as in nature. Even a weak charge on the particles can significantly influence their electric interaction. We investigated the phenomenon of time-dependent electric interaction between two conducting spheres in an electrostatic field. A mirror-image method was developed to analyze this system, and the fundamental role of the charges on the spheres was studied. We concluded that charges conducted to the lower sphere through the alumina tube used in our system play a main role in determining the time-dependent interaction, whereas the influence from air ions is negligible.     

Photonic nanojets as three-dimensional optical atom traps: A theoretical study

We show that an efficient three-dimensional optical atom trap can be achieved by light scattered off a dielectric microsphere. Namely, under suitable conditions, a plane wave incident on a polymer sphere produces a focal point in the forward scattering direction known as photonic nanojet. The photonic nanojet is formed at a distance of a few micrometers away from the surface of the sphere wherein the Casimir–Polder interaction felt by an atom is negligible compared to the optical and gravitational potentials. When many polymer spheres are brought together so as to form a linear chain, a one-dimensional periodic optical lattice filled with cold atoms is possible since interference between the incident and scattered beams is minimal when the spheres are not too close.     

Geometric phases and entanglement of two qubits with XY type interaction

It is shown that geometric phases and entanglement may fail to detect level crossings for two qubits with XY interaction. The rotating magnetic field produces a magnetic monopole sphere like conducting spheres in that only a ground state evolving adiabatically outside the sphere acquires a geometric phase.     

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.     

Detection of low energy scattered X-rays using charged spheres

To detect low energy scattered X-ray dose below 9.5 keV simply, we have designed a low energy X-ray detector that uses multiple electrically charged conductive spheres floated by static electricity repulsion force. This detector detects the dose with the following steps (principles): (1) positive and negative ions are generated by ionization function of low energy X-rays projected in the detector; (2) those ions neutralize the electrically charged conductive spheres floated; (3) accordingly, the spheres fall; and (4) the detector detects low energy X-ray dose from the number of the conductive spheres fallen. This paper verified performance of this detector.     

Motion of a charged particle in the field of a grounded conductive sphere

Motion of a charged particle in the field of a grounded conductive sphere is investigated. It is assumed that the field created by the sphere is quasi-static that implies limitation on particle velocities by nonrelativistic values and the possibility of neglecting magnetic interaction and heat losses. A classification is provided and possible particle trajectories are constructed in the examined case.