叠加法求均匀带电球体电场问题

现有教材中计算均匀带电圆盘轴线电场强度公式,只得到场强大小,没有明确给出场点和圆盘的相对位置与场强方向之间的关系。若根据场强叠加的方法利用此公式计算均匀带电球体的场强分布,容易得到错误的结果。将符号函数引入均匀带电圆盘轴线上电场强度计算式,可以得到场强大小及相对于圆盘的方向,清楚而准确地给出均匀带电圆盘轴线电场强度。利用该公式再次求解均匀带电球体电场,结果与利用高斯定理得到的结果完全相符。     

均匀带电薄圆盘的电场

通过解拉普拉斯方程导出均匀带电薄圆盘的电势和电场的级数表达式,进而讨论均匀带电薄圆盘平面内、中心轴线上和远区的电场。     

均匀带电薄圆盘的电势及等势面

根据电势的叠加原理，导出了均匀带电薄圆盘电势的级数表达式，并进而给出了等势面方程。     

均匀带电圆盘的静电势问题

讨论了均匀带电圆盘静电势问题的两种解法，即延拓法和方程法，澄清了延拓法求解中的一些错误。     

变速旋转均匀带电薄圆盘空间电磁场 的迭代计算

利用场的轴对称性,巧妙联合运用麦克斯韦方程组,以轴线上的场为初值,通过反复迭代的方法,获得了变速旋转的均匀带电薄圆盘空间电磁场的无穷级数表达式。     

有限长均匀带电圆柱面的电场强度和电势

联合使用髙斯定律和静电场的环路定律,以轴线的值为初值,通过反复迭代的方式,巧妙地求出了均匀带电圆柱面空间电场的级数表达式,进而根据电势的定义计算出了空间电势分布。     

Feynman圆盘佯谬与角动量守恒

一、Feynman圆盘佯谬 在《Feynman物理学讲义》第二卷中提出了这样一个佯谬[1],如图1所示,考虑一个无摩擦自由转动的塑料圆盘,圆盘的中部有一个通以稳定电流的细长螺线管,在圆盘的边缘镶上一些带同号等量电荷的金属小球。现在切断电流,这样的操作不致于给圆盘绕轴旋转有什么力矩,因此,似乎圆盘也就不会绕轴旋转。可是根据电磁感应定律,切断电流,磁场消失,在螺线管周围产生涡旋电场,此电场作用于圆盘边缘带电金属小球上的力将使圆盘绕轴旋转。这里就发生了费曼圆盘旋转还是不旋转的作谬问题,费曼在这个佯谬的最后饶有风趣地说:“谁解答了这…     

关于圆盘状物体的几个物理量的计算

在大学物理教学中,关于圆盘状物体的物理量有很多,如电学中带电圆环、带电圆盘,其周围空间产生的电场强度和电势怎样计算？关于铜质圆盘状物体在磁场中转动时产生的电动势的计算问题等;力学中圆盘的转动惯量、椭圆盘的转动惯量,圆盘状物体转动时的摩擦力矩问题、驱动力做功问题等.本文将对这些物理量进行分析,并找出一些共同的规律和特点,将其归纳总结,计算所需要的物理量.     

微元法研究均匀带电体的电场分布

以均匀无限长带电直线的电场分布为基础,运用微元法和叠加原理研究了无限大均匀带电平面和无限长均匀带电圆柱面在其周围电场分布情况。然后根据均匀带电圆环轴线上的电场分布,进一步讨论均匀圆柱面在其轴线上的电场和均匀带电球面在其周围产生的电场,所得结果与高斯定理完全符合。     

费曼圆盘佯谬

该文讨论了一个表现违反角动 量守恒的佯谬问题，指出传给带电圆盘的 角动量是由于电磁感应的结果，本文通过 找出圆盘角动量的来源解决了这个佯谬．     

均匀带电细圆环电场的级数解

根据点电荷场强公式和电场叠加原理,导出了均匀带电细圆环电场的级数表达式,进而讨论了均匀带电细圆环平面内、中心轴线上和远区的电场.     

Coulomb self-energy of a uniformly charged three-dimensional cylinder

We calculate exactly the Coulomb self-energy of a uniformly charged three-dimensional cylinder. We derive a general analytical formula which, in the limit of zero length, gives also the correct result for the Coulomb self-energy of a uniformly charged two-dimensional disk. The exact analytical expression that we derive can be used in models that incorporate finite thickness effects in studies of two-dimensional electronic systems in the fractional quantum Hall regime as well as models that describe cylindrical beams of charged particles, certain colloidal suspensions of charged rigid rod-like particles and biological systems consisting of macromolecules with cylindrical symmetry.     

Distributions of potential and field on central axis line generated by elliptic ring uniformly charged

Using the theory of elliptic integrals and the mathematic trick, we obtain analytic distribution functions of the potential and the field on the central axis line generated by an elliptic ring uniformly charged and we make the discussion about it. The important properties of the potential and the field on the central axis line generated by an elliptic ring uniformly charged is shown.     

均匀带电圆环内点电荷的非线性振荡

本文用数值方法求解含有椭圆积分的二阶微分方程，讨论了均匀带电圆环内点电荷的非线性振荡及其运动特征．     

Coulomb self-energy and electrostatic potential of a uniformly charged square in two dimensions

The most popular model for a two-dimensional electronic system considers electrons moving in a background of uniform positive charge. Studies of finite systems employing a spherical geometry (electrons on the surface of a sphere) or a disk geometry background are numerous. The same cannot be said for a square geometry, who after all, would be the geometry of choice for quantum Hall states in a Landau gauge. A background represented by a uniformly charged square seems to be perceived as too costly from a computational point of view. By using simple transformations, we show that the Coulomb self-energy and the electrostatic potential of a uniformly charged square can be exactly calculated and poses no difficulty. The current results can be used in systematic studies of properties of finite systems of electrons embedded in a positive background in the form of a uniformly charged square.     

The thermodynamic limit for jellium

The thermodynamic limit of the free energy, energy, pressure, and entropy is established for a neutral system of charged particles interacting with a fixed, uniformly charged background (jellium).     

瓣形均匀带电面在其直径处的电势分布

从点电荷的电势计算公式出发推导出了瓣形均匀带电面在其直径处的电势分布.进一步讨论了均匀带电半球面在其底面以及均匀带电球面内部和外部的电势分布.     

圆环电荷的电势的几种算法及讨论

用三种方法计算了均匀带电圆环的电势,并略加讨论.     

Calculation of the Coulomb electrostatic potential created by a uniformly charged square on its plane: Exact mathematical formulas

We calculate exactly the Coulomb electrostatic potential created by a uniformly charged square on its plane. The chosen solution method leads to certain types of integral expressions which involve combinations of products of error functions and power functions. These type of integrals that should be solved are not standard ones, therefore, the integration formulas we derive in the process may be deemed of mathematical interest on their own right. Use of these formulas enables us to derive an exact analytic expression for the Coulomb electrostatic potential created by a uniformly charged square at an arbitrary point on its plane.     

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