摘要
带电偏心圆柱面有内偏心和外偏心两种情况,它们都有相同的对称点公式。通过保角变换将两种偏心区域变换成环形区域,求出环域的两个半径,并做了详细分析。用简单方法求出电势函数,进而求出电场强度的两个分量和电通函数。将公式无量纲化,用MATLAB绘制图形,证明了等势线和电场线都是圆,发现了偏心圆柱面的电场等效于两条等量异号无限长带电直线产生的电场。
There are two cases for the charged eccentric cylindrical surface:internal eccentricity and external eccentricity,both of them have the same formula for symmetry point。The two eccentric regions are transformed into annular regions by conformal transformation,and the radii of the two annular regions are calculated and analyzed in detail.The electric potential function is obtained by a simple method,and then the two components of the electric field strength and the electric flux function are obtained.The formulas are nondi⁃mensionalized,and the graphs are drawn by using MATLAB,so as to illustrate the results.It is proved that both the equipotential lines and the electric field lines are circles.Moreover,it is found that the electric field of the eccentric cylindrical surface is equivalent to the electric field generated by two infinitely long straight lines with equal number of charges but different signs.
作者
周群益
莫云飞
周丽丽
Zhou Qunyi;Mo Yunfei;Zhou Lili(College of General Education,Guangzhou Institute of Science and Technology,Guangzhou Guangdong 510540,China;School of Electronic Information and Electrical Engineering,Changsha University,Changsha Hunan 410022,China;School of Medical and Information Engineering,Gannan Medical University,Ganzhou Jiangxi 341000,China)
出处
《衡阳师范学院学报》
2023年第3期43-50,共8页
Journal of Hengyang Normal University
基金
国家自然科学基金(12004053)
广东省高校科研特色创新项目(2020KTSCX209)。
关键词
偏心圆柱面
保角变换
电势函数
电场函数
等势线
电场线
eccentric cylindrical surface
conformal transformation
potential fuction
electric field function
equipotential line
electric field lines
