避雷针旁的电场分布
论文编号:WLX054 字数:8602,页数:21摘 要 本论文研究的是避雷针旁的电场分布。避雷针是一种用在高层建筑上防止雷击的装置。一般来说空中带电雷云在没有与其他异性带电物体放电时，它所带的电是静电。我们将避雷针看成是放在雷云静电场中的接地圆锥导体，这样所研究问题就转化为求静电场中导体表面区域内的电场分布问题。根据电磁场的基本理论麦克斯韦方程组和导体的静电条件得到导体表面的边界条件。用分离变量法求解拉普拉斯方程满足边界条件的解，通过计算得到避雷针尖端附近的电场强度，用电动力学的理论分析解释了尖端放电的原理从而能更好的分析避雷针的工作原理。最后用MATLAB模拟仿真，可以更直观的看到避雷针尖端附近区域电场的强弱分布状况。关键词：避雷针 静电场 麦克斯韦方程组 拉普拉斯方程 尖端放电 MATLAB仿真Abstract This paper study of electric field distribution near a lightning rod。Lightning rod is a device which is used to prevent high-rise buildings from lightning strikes. Generally speaking, thundercloud in the air has electrostatic energy when it has not discharged with other objects which have charges of different polarity with it. By regard the lightning rod as a grounding conical conductor in the electrostatic field of thundercloud，we can transform the problem which we study into a problem of solving the electric field distribution in the surface of a conductor in the electrostatic field. We can get boundary conditions based on maxwell equations and electrostatic conditions of conductor. The paper gives solutions of laplace equations satisfy boundary conditions by separation of variables and electrical field strength near the tip of lightning rod by calculating，and analyzes principle of point discharge according to electrodynamics theory to make a better study of working principle of lightning rod. We can have a more intuitionist observation of electric field distribution near the lightning rod by MATLAB simulation.Keywords：Lightning rod；Electrostatic field；Maxwell's equations；Laplace equation；point discharge；MATLAB simulation目 录中文摘要i英文摘要ii目录iii第一章 绪论 11.1研究动机和目的1 1.2研究背景11.3 MATLAB工具介绍21.4论文内容概述2基本原理3 2.1麦克斯韦方程组3 2.2静电场4 2.3拉普拉斯方程 分离变量法5理论计算7计算机模拟10结论13致谢 14参考文献15附录 MATLAB程序16
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