【作者】 杨英；

【导师】 胡先权；

【作者基本信息】 重庆师范大学 ， 课程与教学论， 2006， 硕士

【摘要】 本文通过研究静电场等势线和电力线的求解与描述以及电偶极子的电荷禁闭,领悟到了现代物理教学的新发展,但同时也发现了物理教学中存在的一些问题。电磁场理论教学中虽然教材繁多,但这些教材里的知识面比较窄,还有不少的佯谬问题还有待于从更高的层面自洽地加以解释。针对上述存在的问题,如何把物理上的新知识,新概念反映到物理教学中去,如何在物理教学中培养学生的科学素质和创新能力是物理教学的首要问题。本文就电磁场中静电场求解的几个典型疑难问题进行分析、讨论望能对电磁场理论教学有所裨益。论文主要是针对几种不同边界条件下的平面场求解进行研究。在通常的电磁学教材中,最基本平面场的求解方法是电场迭加原理,这种方法虽然应用广泛,但对于一些复杂的边值问题,求得的只是形式解。而本文主要运用一些带有特定技巧的计算方法求解一些边界形状比较复杂的平面场问题。对二维拉普拉斯方程或泊松方程的平面场的解法有多种,如分离变量法、格林函数法或者其他方法,但如果它们的边界形状比较复杂,用这些通常的方法求解会非常困难,即使对于存在有解析解的特殊情况,一般说来也不可能求出,而且求得的只能是近似解。偏心圆柱面与分离圆柱面带电导体的电场以及角形区域内的静电场,还有带电导体圆柱位于接地导体附近的静电场的求解问题都属于这种情形。保角变换法和电像法是带有特定技巧的求解平面场的计算方法,如果使用得好,可以弥补分离变量法等方法的不足,而且可以使复杂的静电场边值问题的求解大为简化,如果采用和计算软件包相结合,还可以得到泊松方程在数学物理方法教材中难得一见的可视化结果。本文研究的带电导体圆柱位于接地导体平面附近时的静电场和角域场内的静电场就属于这种情形。电像法还是唯一性定理的一个重要应用,采用分离变量法和镜像法相结合,可找到所求的静电场所满足的泊松方程,从而求得电势,例如本文中导体壳内的电偶极子电荷禁闭的电势表达式的求解更多还原

【Abstract】 This article through studying on the solution and description of the Equipotential line and Power line for the static field and electrostatic shielding partial contents, comprehended recent development in modern physics teaching, as well as problems. Although there are many teaching materials about the theory of electromagnetic, the range of knowledge is not wide and there are many paradoxical questions to be explained from a higher stratification. In view of the above questions, what problems people should firstly resolve in physics teaching are how to put the new knowledge、new concept of physics into practice of physics teaching, and how to foster students’scientific quality and the innovation ability. This article analyses and discusses several typical difficult problems related to the solution of the electromagnetic field in electrostatic field, which will benefit the teaching of the theory of electromagnetic field.This paper mainly aims at the research into the solutions of the electrostatic field when facing several kinds of different boundaries. In the electromagnetics teaching materials, the most basic solution method of the electrostatic field is the electric field principle of superposition. This method is employed widely, but regarding some complex boundary-value question, it only obtains the formal solution. This article mainly utilizes some computational methods with specific skills to solve some electrostatic field questions with quite complex boundary shape. There are many kinds of ways to solve the electrostatic field of two-dimensional Laplace’s equation or the Poisson’s equation, like the separation of variables, Green’s function or alternative means. But if their boundary shapes are quite complex, it is extremely difficult to use these usual methods, and, in general, it is impossible to work out even there is such peculiar instance as analytic solution, or obtains the approximate solution. The static electricity field for two parallel cylinders with eccentric axes or separated ,angular space, along with solution of the charged conductor of cylinder all can be explained by this kind of situation.The conformal mapping method and the electrical images are the computational methods with specific skills, to solve problems in the electrostatic field. If use well, they更多还原