多重镜像法求解三带电金属球的电场

镜像法是求解静电场的一种基本方法.本文通过电容法和电荷法两种方法来求解三金属球体系的多重镜像电荷,进而将带电金属球在空间的电场替代为各个等效电荷和镜像电荷产生的电场.通过对比电场的分布,验证了两种方法的正确性和一致性.进一步的研究结果表明,调节第三个金属球的位置和带电量可以实现两金属球之间的相互作用力由吸引向排斥的转变.结合Matlab软件,我们直接给出了双球和三球体系时电势在空间的分布.     

利用镜像法求解劈形导体边界的讨论

镜像法是解析求解高对称性静电场边值问题的一种简便方法.本文研究劈形边界导电系统的镜像问题，此时导电劈的夹角α存在附加条件α=π/n(n=2,3,4,...),该附加条件是教学过程中学生的疑问点.镜像法求解静电问题的理论依据是唯一性定理，在保持边界条件与边值关系不变的原则下，推导导电劈夹角α的数学表述并解释分析其存在附加条件的原因.     

线电荷与圆柱导体间的相互作用

利用镜像法,在计算线电荷与接地圆柱导体间的相互作用的基础上,通过增加镜像电荷的方法,进一步分析求解得出了线电荷与绝缘圆柱导体、与电源连接的圆柱导体间的相互作用.     

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.     

螺绕环磁场的镜像对称性分析

利用安培环路定理求解长直导线、长直螺线管、螺绕环等载流系统的磁场时,对称性分析是选取闭合回路的关键.通过分析解螺绕环磁场时的镜像对称条件,说明合理应用对称性分析,能够使求解电场和磁场问题的图像更清晰、计算更简化、表述更准确.因此,在电磁学教学中应给予对称性分析足够的重视.     

基于镜像电荷法探测液氦表面电子的自旋态

文献[Phys.Rev.A,2006,74:052338]的理论研究表明液氦上电子自旋具有长达100秒的相干时间,因此在实施量子信息处理方面具有很大的应用前景.然而,这一理论还未得到实验的证实.液氦上电子的自旋-轨道耦合可以为电子自旋探测提供一种可选的方法.理论上,电子自旋-轨道耦合可以由液氦膜下方的微电极电流产生.在微波驱动下,电子发生电偶极跃迁,导致电子距离液氦表面的平均高度发生改变.利用镜像电荷法[Phys.Rev.Lett.,2019,123:086801],电子的这种轨道运动可以被实验测量.建立基于液氦上电子-自旋轨道耦合的密度矩阵方程,并数值求解镜像电荷的振动行为.结果表明不同的自旋态将会引起不同的感应电流,这种差异提供了一种可选的电子自旋探测方法.     

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。     

对《 镜像电荷求能量方法辨析》 一文的两点商榷

指出《 镜像电荷求能量方法辨析》 一文存在的两个隐蔽性较高的问题, 与各位同行交流探讨     

镜像系统和镜像天线

对电荷电流体系在理想导体平面所形成的镜像系统的各物理量作了全面分析，并得出镜像天线的结果。     

点电荷和介质球系统的镜像电荷分布

用镜像法处理介质中的静电问题,一般书刊上只论及到两种情形:一是两均匀电介质交界面为一无限大平面,在其中一种介质中有一点电荷;二是无限长均匀电介质圆柱置于另一均匀介质之中,在圆柱内或圆柱外有一与其轴线平行的无限长线电荷.在这两种情形中,电势都可以用简单的镜像系表示     

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.     

Nonstandard electrostatic problem for strips

The spatial field distribution is the most frequent subject of standard electrostatic analysis. In this paper the system of several strips in external spatial-harmonic electric field, which causes the charge distribution on them, is considered. The solution is constructed as a linear combination of certain template functions, evaluated in spectral domain and satisfying the electric boundary conditions on the strips. The problem is analogous to wave scattering; this justifies the application of the wave-scattering terminology (i.e. incident wave for the external field and the corresponding ‘radiation condition’) in the considered nonstandard ‘electrostatic scattering’ problem. The strip total charge and the Bloch harmonics of the ‘scattered’ field are evaluated.     

Electric field and the charge distribution on the surface of an insulator in a vacuum

The free charge steady-state distribution over the insulator surface that arises in a strong electric field in a vacuum can be found by solving the boundary-value problem for the electrostatic field strength if the angle between the field vector and vacuum-insulator interface is given. A general solution to this boundary-value problem is derived for the case of an in-plane field and rectilinear interfaces. Laws of charge and field formation that follow from the solution obtained are considered. Formulas for the electric field strength and charge density in terms of elementary functions are obtained for a number of particular cases. Power-type expressions for the electric field and a critical angle between the electrode and insulator surface that describe the field behavior and charge distribution near the vacuum-insulator-electrode contact are derived.     

电子全息法观测点电荷微电场分布及荷电量

本文采用一种简易制备静电场样品的方法,基于以下物理事实:一个置于薄导电碳膜上的非导电粒子,例如直径为0.31μm聚乙烯乳剂小球,在电镜中观察时,由于静电积累效应,它将成为一个荷电体,很显然,这个荷电体带有正电量Q,并能用一个点电荷场来模拟这个合成电场.采用这个模型,能用电子全息法观测由该点电荷所形成的静电场分布及荷电量的大小.     

The Method of Images applied to the grounded sphere: The problem of the ground wire

The Method of Images poses an important difficulty when used to solve the problem of a charge in the presence of a grounded conducting sphere. This arises from the fact that the sum of the inducing charge and the image charge is different from zero. As a consequence, there is a monopole field far from the system, and any ground wire physically connected to the sphere will carry an electric current, changing the initial balance of charges until a new equilibrium is reached. The approach taken in this paper assumed an infinite straight wire connecting the sphere to ground. The charge distribution over the surface of the conductors was calculated, and the results analyzed. It was shown that the thinner the wire, the lower will be its total charge, and the closer will be the calculated charge density at the surface of the sphere to the conventional solution by the Method of Images.     

电子全息法及其在观测微电场分布中的应用

介绍了电子全息术的工作原理以及制备静电场样品的新方法:一个置于薄导电碳膜上的非导电粒子,例如直径为0.31μm聚乙烯乳剂小球,在电子显微镜中观察时,由于静电积累效应,它将成为一个荷电体,这个荷电体带有正电量Q,并能用一个点电荷场来模拟这个合成电场。采用这个模型,能用电子全息法观测由该点电荷形成的静电场分布及荷电体大小。 关键词：     

An overlooked electrostatic force that acts on a non-charged asymmetric conductor in a symmetric (parallel) electric field

Usually, when a material that has charge Q is placed in an electric field E, an electrostatic force F = QE acts on the material. This force does not act on a non-charged material. Nevertheless, when a non-charged material is placed in a convergent field, another electrostatic force acts. This force is called the gradient force. If the material is small and the shape is a sphere, the gradient force can be calculated by an approximate formula, but it cannot be calculated for other shapes. In this paper the gradient force that acts on a symmetric rod conductor in a convergent (asymmetric) field was simulated by an axis symmetry finite difference method.Under same simulation conditions without the next two points, the shape of the conductor and the form of the field were reversed. The shape of the conductor was changed into an asymmetric shape (e.g. bat shape), and the form of the field was changed into a symmetric (parallel) one. The electrostatic force that acts on the asymmetric conductor in the symmetric (parallel) field was simulated. It was found that approximately the same intensity force as in the first simulation also acts on this conductor. This force is thought to be an overlooked electrostatic force. I provisionally call it the asymmetric force in this paper.The asymmetric force with differently shaped conductors was simulated and it was found that the asymmetric force was maximized for a cup shaped conductor.Finally, the asymmetric force with the cup shaped conductor in normal and reversed parallel (symmetric) fields was simulated, and it was confirmed that the asymmetric force remains the same in both fields.     

激光等离子体相互作用的局域振荡电子加热机制

 用2.5维粒子模拟程序模拟了超强激光与等离子体的相互作用过程，发现超强激光可以通过J×B加热机制加速电子并引起电荷分离，从而产生很强的静电场并形成电场势阱，电子在静电场势阱中振荡，被多次加速，使得高速电子被甩出势阱，进而增强电荷分离，然后静电场结构被破坏，静电势能传给电子。在此过程中，电子在此阱中作局域振荡，并且被J×B机制多次加速，激光的能量会有效地传给电子，使电子能量高达10MeV。这是一种新的电子加热机制，称之为局域振荡电子加热机制。     

盐离子对蛋白质带电特性的影响

本文应用分子理论,研究盐离子对蛋白质带电特性的影响,理论模型考虑蛋白质与阴离子的结合作用。研究发现,由于蛋白质与阴离子的结合,距离蛋白质表面附近处的阴离子被吸附在了蛋白质表面,在距离蛋白质表面附近区域,阴离子分布较少。通过计算体系中的静电势,我们发现,在距离蛋白质表面附近,静电势呈现了较大的负值,带正电荷的阳离子感受到静电吸引,会出现在距离蛋白质表面附近的区域,这会使得在距离蛋白质表面附近的区域,阳离子数目增多。这样,在不同阴离子浓度、以及阴离子与蛋白质不同结合能条件下,阴离子会在不同程度上影响蛋白质的带电特性、影响体系中的静电特性。通过考察不同结合能条件下,蛋白质表面电荷面密度随阴离子浓度的变化关系还发现,较大的结合能会使得阴离子与蛋白质结合增快,蛋白质表面会呈现从正电荷态向负电荷态的转变。理论结果符合实验观测,由此表明,盐离子与蛋白质的结合导致蛋白质表面带电特性的改变,是盐离子影响蛋白质带电特性的本质。     

Electrostatic field calculation in air gaps with a transverse layer of dielectric barrier

In this paper the influence of transverse layer of dielectric barrier to the electrostatic field strength of air gaps using a hyperbolic needle-to-plane configuration is investigated. A three dimensional field problem is presented for simulating the electrostatic field in the air gap. This is achieved by using the charge simulation method. Group of ring charges are used to simulate the needle surface. A genetic algorithm is used for optimum number, location, dimension and value of simulating ring charges. The used needle tip radius was 8 μm while the gap spacing varied from 0.3 cm to 50 cm. The optimum barrier position minimizes the maximum electrostatic field and the electric energy density at the needle tip and consequently maximizes the required breakdown value. The simulation result has been compared with available experimental observations. A good agreement is found between the numerical and experimental data.