浅论均匀带电球冠和相切平面的电场等价性

大学物理中不同带电体的电场等价性,能够较好地训练物理学习者的分析和解决复杂实际问题的逻辑思维,从而提高物理知识的具体应用能力.本文首先讨论了均匀带电球冠面和与之相切的均匀带电平面在球面北极点的电场等价性,然后证明了均匀带电圆弧和与之相切的均匀带电直线在圆环顶点处的场强是不等价的,并且指出只有引入随角度变化的电荷线密度才...     

探究均匀带电直线和圆弧产生电场的关系

利用微元法和对应性推证了均匀带电直线与均匀带电圆弧产生的电场等效; 利用微元法和对称性推 导了均匀带电圆弧在圆心的场强公式; 利用结论巧妙解答有关线性带电体的场强计算问题     

用微元法讨论旋转均匀带电球的磁矩

以旋转均匀带电球为例,利用微元分析法讨论磁矩的计算,从而凸显微元选择的重要性和灵活性.     

关于均匀带电球面上电场强度的求解

由于均匀带电球面上的电场强度无法用高斯定理求出,现行大部分大学物理基础教材在讨论均匀带电球面产生的场强分布时,只用高斯定理求出了该带电系统内外空间电场的分布,并没有给出球面上场强的计算方法,只是指出在球面上场强值不连续.文章利用叠加原理和电容器能量的变化两种方法分别导出了均匀带电球面上任一点的场强值,验证了均匀带电球面的场强是不连续的,两种方法思路截然不同,但得到的结果完全相同,该结果使得高斯定理求出的均匀带电球面在空间电场分布的结论更加完整.     

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。     

为什么带电圆环中心处电场线最密而场强为零

由均匀带正电圆环的电势,画出带电圆环内侧电场线分布,可知圆环的圆心处电场线最密集即场强"最大",而根据场强的矢量合成得出的结论是圆环的圆心处场强应为零.那么,均匀带电圆环内侧平面内电场线的真实分布应该是如何?本文给出了详尽的分析.     

瓣形均匀带电面和均匀带电体在其球心处的电场

在大学物理课程电磁学部分的教学中,经常会利用高斯定理研究均匀带电球面、均匀带电球体等电荷分布具有高度对称性的带电体的电场分布.对于这些均匀带电球面、均匀带电球体的一部分,比如瓣形均匀带电面和瓣形均匀带电体,利用高斯定理不能求出其电场分布,但是可以利用点电荷的电场强度公式加电场叠加原理的方法研究在一些特殊位置的电场.本文推导出了瓣形均匀带电面和瓣形均匀带电体在特殊点球心处的电场,并且进一步讨论了均匀带电半球面、球面、半球体和球体在球心处的电场.     

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.     

均匀带电圆环片的空间静电场

通过点电荷的电势公式,利用叠加原理及勒让德多项式与母函数的关系,计算出了均匀带电圆环片在空间产生的电势及场强,并对结果进行了讨论.     

电各向异性介质中带电圆环的电势和场强

由电各向异性介质中连续带电体的电势公式,利用积分的方法,求得放置在电各向异性介质中的均匀带电圆环在其轴线上所激发的电势,并进而求得在其轴线上激发的场强。对求得的结果进行讨论,可得到在电各向异性介质中均匀带电圆环在其轴线上所激发的电势和场强的一些的特点。     

Development of a numerical model for the electric current in burner-stabilised methane–air flames

This study presents a new model to simulate the electric behaviour of one-dimensional ionised flames and to predict the electric currents in these flames. The model utilises Poisson’s equation to compute the electric potential. A multi-component diffusion model, including the influence of an electric field, is used to model the diffusion of neutral and charged species. The model is incorporated into the existing CHEM1D flame simulation software. A comparison between the computed electric currents and experimental values from the literature shows good qualitative agreement for the voltage–current characteristic. Physical phenomena, such as saturation and the diodic effect, are captured by the model. The dependence of the saturation current on the equivalence ratio is also captured well for equivalence ratios between 0.6 and 1.2. Simulations show a clear relation between the saturation current and the total number of charged particles created. The model shows that the potential at which the electric field saturates is strongly dependent on the recombination rate and the diffusivity of the charged particles. The onset of saturation occurs because most created charged particles are withdrawn from the flame and because the electric field effects start dominating over mass based diffusion. It is shown that this knowledge can be used to optimise ionisation chemistry mechanisms. It is shown numerically that the so-called diodic effect is caused primarily by the distance the heavier cations have to travel to the cathode.     

基底性质对二维层状电子气感应电场的影响

采用线性化量子流体动力学模型,研究了载能粒子与二维层状电子气相互作用时的集体静电激发现象。在适当的边界条件下推导出感应电势,入射粒子所受的阻止力和侧向力的一般表达式,讨论了存在绝缘基底情况下基底介电常数对感应电势、阻止力及侧向力的影响。结果表明:当入射粒子速度较小时,基底的极化电场较弱,其介电常数的变化对感应电场几乎无影响,而当速度较高时因极化电场较强而影响很大;入射粒子距离与基底相连的电子气平面越近,基底介电常数对各物理量的影响越大。     

光学渡越辐射理论及其在直线感应加速器脉冲电子束诊断中的应用

匀速运动的带电粒子在穿过具有不同介电常数的两种媒质界面时要产生所谓光学渡越辐射。该辐射在粒子的入射平面上呈偏振行为;从辐射强度的角分布可以确定入射粒子的能量。在入射到双膜系统的情况下,由于干涉的发生,在第二膜前表面的强度角分布有振荡行为。利用这些现象,可对脉冲电子束包络半径、束电流密度的横向分布,束能量以及横向散角进行测量,依照这一原理在各LIA加速器上进行的脉冲电子束参数测量,获得的有效数据极大地提高了加速器的调试效率。     

数值积分求解均匀带电圆环平面上的电场分布

本文用数值积分的方法计算椭圆积分，求出在均匀带电圆环平面上的场强与电势．     

Electromagnetic scattering of charged particles in a strong wind-blown sand electric field

Some field experimental results have shown that the moving sands or dust aerosols in nature are usually electrified,and those charged particles also produce a strong electric field in air, which is named as wind-blown sand electric field.Some scholars have pointed out that the net charge on the particle significantly enhances its electromagnetic(EM) extinction properties, but up to now, there is no conclusive research on the effect of the environmental electric field. Based on the extended Mie theory, the effect of the electric field in a sandstorm on the EM attenuation properties of the charged larger dust particle is studied. The numerical results indicate that the environmental electric field also has a great influence on the particle's optical properties, and the stronger the electric field, the bigger the effect. In addition, the charged angle, the charge density, and the particle radius all have a specific impact on the charged particle's optical properties.     

Invariant noncanonical mappings of singular theories. II

In a paper of the same title published in Physical Revview Dit was shown that in singular theories (i.e. theories incorporating constraints) non-canonical infinitesimal mappings that map equivalence classes intact on each other lead to the divergence of a vector field associated with the mapping constant throughout the equivalence class. The infinitesimal mappings form the germ of the group of finite mappings of equivalence classes on each other that change the form of the symplectic tensor field. Any non-canonical coordinate system on phase space thus obtained defines a scalar density field that is constant over an equivalence class. The constant of the motion obtained earlier represents the infinitesimal deviation of this new field from unity.     

Space-time structure and bound-charge fields

Together with a “postulate of equivalent situations,” the exact solution for the field of a charge in a uniformly accelerated noninertial frame of reference (NFR) makes it possible to find the space-time structure and fields of charged conductors of arbitrary shape without using the Einstein equations. The energy of the electric field outside of a charged plane, which is equal to the rest energy of the masses of the charges creating the field, is determined. The space-time metric outside of the charged plane is established; it could also have been found from the exact solution of the Einstein-Maxwell equations. This solution describes the equilibrium of charged dust in parallel electric and gravitational fields. The field and metric are found outside of a charged conducting sphere. While it eliminates the self-energy divergence, the proposed method renders the classical electrodynamics internally consistent on transition to any short distance. All-Russian Scientific Research Institute of Opticophysical Measurements. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 63–74, October, 1997.     

均匀带电平面折线在空间产生的电场及其可视化

推导了均匀带电线段在二维平面中产生的电势的简要公式,进而推导了在三维直角坐标系中的电势公式,形成了带电折线(包括任意多边形)的电势简要公式.根据电势与电场强度之间的关系,列出了场强的表达式.将公式无量纲化,利用MATLAB指令,绘制了各种形状的带电多边形和折线的等势面和三维电场线,并显示了电场在空间的分布规律.     

一种基于旋转调谐的超材料

数值仿真研究了一种可调谐的双开口谐振环(DSRR)超材料.在平行入射的电磁波激励下,这种DSRR单元可以在不同的频段分别表现出磁谐振和电谐振.当外加电场E与DSRR的双开口平行时,DSRR受激励得到的磁谐振和电谐振强度最大.随着DSRR超材料沿外加磁场H方向顺时针旋转,其磁谐振和电谐振频率基本保持不变,但谐振强度均发生显著下降,同时对应透射相位的突变也逐渐降低.提出的超材料调谐方法只需要简单地旋转材料,而不需要改变原有超材料单元的结构或者增加额外的激励场,极大地简化了可调谐超材料的制备及应用,在电磁开关、相位调制等方面具有潜在的应用.同时,这种简单的方法有希望应用于更高频段的超材料调谐,可以有效地拓展太赫兹频段和光频段超材料的实际应用.