电荷投影法在研究无限长导体薄板电荷分布规律中的应用

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1. 广州理工学院，广东广州510540; 2. 长沙学院电子信息与电气工程学院，湖南长沙410022; 3. 赣南医学院医学信息工程学院，江西赣州341000; 4. 长安大学理学院应用物理系，陕西西安710064

周群益( 1955—) ，男，湖南衡阳人，广州理工学院副教授，主要从事凝聚态物理研究工作.

收稿日期: 2020-12-23

修回日期: 2021-02-21

网络出版日期: 2021-07-08

基金资助

广东省高校科研特色创新项目( 2020KTSCX209) ; 国家自然科学基金( 12004053) 资助

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Application of charge projection method in the study of charge distribution law of infinitely long conductor thin plate

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1. Guangzhou Institute of Science and Technology，Guangzhou，Guangdong 510540，China; 2. School of Electronic Information and Electrical Engineering，Changsha University，Changsha，Hunan 410022，China; 3. School of Medical and Information Engineering，Gannan Medical University，Ganzhou，Guangdong 341000，China; 4. School of Science，Chang’an University，Xi’an，Shaanxi 710064，China

Received date: 2020-12-23

Revised date: 2021-02-21

Online published: 2021-07-08

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利用无限长均匀带电圆柱面的电荷分布规律和无限长带电直线的场强公式，采用电荷投影法推导了有限宽无限长

带电导体的面电荷分布规律.根据电势叠加原理推导了电势积分式，利用场强与电势之间的关系推导了电场强度两个分量的

积分式.将公式无量纲化，通过数值积分计算了电势和场强的分量之值.通过作图，显示了有限宽无限长带电导体薄板的电势

和场强，画出了二维等势线和电场线，充分显示了场强的分布规律.

关键词： 带电导体薄板; 电势; 电场强度; 无量纲作图

周群益, 莫云飞, 周丽丽, 侯兆阳 . 电荷投影法在研究无限长导体薄板电荷分布规律中的应用[J]. 大学物理, 2021 , 40(7) : 19 . DOI: 10.16854 /j.cnki.1000-0712.200545

Using the charge distribution law of a uniformly charged cylinder of infinite

length and the field strength formula of an infinitely long charged straight line，and adopting

the charge projection method，the surface charge distribution of a charged conductor of finite

width and infinite length has been deduced. According to the principle of electric

potential superposition，the electric potential integral formula is derived; using the relationship

between field strength and electric potential，the integral formula of the two components of

electric field strength is derived. The formula is dimensionless，and the values of the components

of electric potential and field strength are calculated through numerical integration. The

electric potential and field strength of the charged conductor sheet of finite width and infinite

length are shown in the picture，and the two-dimensional equipotential lines and electric

field lines are also drawn in the diagram，which fully shows the distribution law of field strength.

Key words： charged conductor sheet; electric potential; electric field strength; dimensionless drawing

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