《电力线之美.ppt》由会员分享,可在线阅读,更多相关《电力线之美.ppt(34页珍藏版)》请在三一文库上搜索。
1、电力线之美,PB01203064 王泉,问题的提出,电场线是美的,问题的提出,电场线是美的 电场线是怎么绘制出来的?,电场线方程(1),电场线的定义:电场所在空间中的一系列想象的曲线,曲线上每一点的切线方向都与该点的场强方向一致。,定义,数学化,抽象,电场线方程(1),电荷 (Q1,Q2Qn),库仑定律,叠加原理,空间各点的场强(大小,方向),电场线方程(1),电场线方程(1),孤立点电荷的电场线方程 :,电场线方程(1),复杂一些的情况 :,?,电场线方程(2),数值方法(欧拉折线法),基本思想: 寻求精确解的折线逼近,电场线方程(2),流程:,点A (x,y),以A为起始点,A的切线方向为
2、方向,以s为步长作线段,A的切线方向,电场线方程(2),电场线方程(2),例: 线性电四极子 (位于 N(-L,0), O(0,0), P(L,0),带电量分别为 + Q,-2Q, + Q的电荷系统 ),思想:欧拉折线法 初始条件:在距离电荷很近的地方取点,程序流程图(Start),YES,NO,NO,YES,注: 1.测试点A带一个单位正电荷 2. 代表测试点A要走的方向 3.Points为存储A所经过的点的数组 4.Graphic为存储场线的数组 5.测试点A满足的条件:不能离电荷太近 不能离远点太远,程序流程图(End),一些电场线(线性四极子),令: PositiveCharge =
3、2 + 0i, 1; NegativeCharge = -2 + 0i, 1; MiddleCharge = 0 + 0i, -2;,坐标,带电量,Generated By Mathematica 4.1,一些电场线,令: PositiveCharge = 2 + 0i, 1; NegativeCharge = -2 + 0i, 1; MiddleCharge = 0 + 0i, 0;,Generated By Mathematica 4.1,一些电场线,令: PositiveCharge = 2 + 0i, 1; NegativeCharge = -2 + 0i, -1; MiddleCha
4、rge = 0 + 0i, 0;,Generated By Mathematica 4.1,一些电场线,令: PositiveCharge = 2 + 0i, 3; NegativeCharge = -2 + 0i, -1; MiddleCharge = 0 + 0i, 0;,Generated By Mathematica 4.1,一些电场线,令: PositiveCharge = 2 + 3i, 5; NegativeCharge = -2 + 0i, -1; MiddleCharge = 0 + 0i, 0;,Generated By Mathematica 4.1,一些电场线(平面电三
5、极子),令: PositiveCharge = 2 + 0i, 1; NegativeCharge = -2 + 0i, 1; MiddleCharge = 0 + 3.4641i, -2 ;,Generated By Mathematica 4.1,一些电场线,令: PositiveCharge = 2 + 0i, 1; NegativeCharge = -2 + 0i, -1; MiddleCharge = 0 - 4i, -5;,Generated By Mathematica 4.1,一些电场线(电偶极子),令: PositiveCharge = 0.1 + 0i, 1; Negati
6、veCharge = -0.1 + 0i, -1; MiddleCharge = 0 + 0i, 0;,Generated By Mathematica 4.1,一些电场线(平面电四极子),令: PositiveCharge = 1 + i, 1; NegativeCharge = -1 + i, -1; PositiveCharge2 = -1 - i, 1; NegativeCharge2 = 1 - i, -1;,Generated By Mathematica 4.1,一些电场线,令: PositiveCharge = 0.5 + 0.5i, 1; NegativeCharge = -
7、2 + 2i, -5; PositiveCharge2 = -0.5 0.5i, 1; NegativeCharge2 = +2 - 2i, -5,Generated By Mathematica 4.1,一些电场线,Generated By Mathematica 4.1,令: PositiveCharge = 1 + i, 1; NegativeCharge = -1 + i, -1; PositiveCharge2 = -3 3i, 1; NegativeCharge2 = +3 - 3i, -1,一些电场线(任意情形),Generated By Mathematica 4.1,令: P
8、ositiveCharge = 3 + 0i, 1; NegativeCharge = -3 + 2i, -3; PositiveCharge2 = -4 4i, 1; NegativeCharge2 = 2 - 3i, -2,等势曲线,等势曲线与电场线曲线正交,作电场线图的过程中把方向角加上/2,所得到的图形就是等势曲线,算法:,一些等势曲线,令: PositiveCharge = 2 + 0i, 1; NegativeCharge = -2 + 0i, -1;,Generated By Mathematica 4.1,一些等势曲线,Generated By Mathematica 4.1,
9、令: PositiveCharge = 2 + 0i, 1; NegativeCharge = -2 + 0i, 1;,一些等势曲线,Generated By Mathematica 4.1,令: PositiveCharge = 2 + 1i, 2; NegativeCharge = -2 + 0i, -1;,一些等势曲线,Generated By Mathematica 4.1,令: PositiveCharge = 2 + 0i, 1; NegativeCharge = -2 + 0i, 3;,总结,数值解法的强大威力(“笨” 但是 有效),Mathematica 编程的优越性(切中要害),谢谢!,参考资料: 1. 电磁学高等教育出版社 2. 数学实验高等教育出版社 3. Fields and Potentials from Point Charges by Department of Physics and Astronomy, Oberlin College,指导教师: 叶邦角,
链接地址:https://www.31doc.com/p-2576129.html