教学讨论

平行板电容器的尺寸效应

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  • 1. 西安交通大学城市学院电信系,陕西西安710018; 2. 西安交通大学城市学院物理教学部,陕西西安710018
曹小鸽( 1985—) ,女,河南许昌人,西安交通大学城市学院电信系讲师,硕士,主要从事电路、工程电磁场等课程的教学和相关的研究工作.

收稿日期: 2020-07-17

  修回日期: 2020-09-25

  网络出版日期: 2021-03-19

基金资助

陕西省教育厅专项科研计划项目( 18JK1032) 资助

The size effect of parallel-plate capacitor

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  • 1. Department of Electrical and Information Engineering; Xi’an Jiaotong University City College,Xi’an,Shaanxi 710018 2. Department of Physics Education,Xi’an Jiaotong University City College,Xi’an,Shaanxi 710018

Received date: 2020-07-17

  Revised date: 2020-09-25

  Online published: 2021-03-19

摘要

本文分别研究了平行圆形板和矩形板电容器的电容随其尺寸变化的规律.对于每种电容器,首先假设电荷在极板上

均匀分布,由此能较简便地得出电容的近似值,然后用Ansoft 软件作有限元仿真,得出更精确的数值.通过对比发现,用均匀带

电近似得出的结果能够正确地反映电容随其尺寸变化的趋势,优于教科书中的平行板电容器公式; 但其数值偏小,原因在于

电荷在极板上并非严格地均匀分布,而是中间少、边缘多.

本文引用格式

曹小鸽, 杨杨 . 平行板电容器的尺寸效应[J]. 大学物理, 2021 , 40(3) : 8 -11 . DOI: 10.16854 /j.cnki.1000-0712.200308

Abstract

It is investigated in this paper how the capacitance of parallel circular-plate and rectangular-plate

capacitors varies with the size,respectively. For each kind of capacitor,first it is assumed that charge is distributed

uniformly on the plate,then approximate values of capacitance can be obtained conveniently,afterwards more accurate

values are obtained via finite element simulation using Ansoft. By comparison,it is discovered that results obtained

using the approximation of uniform charge distribution can reflect correctly the tendancy how the capacitance

varies with the size,which is better than the capacitance formula of parallel-plate capacitor in textbooks; however,

those values are smaller,since charge is not strictly distributed uniformly on the plate,but less in the middle and

more on the edge.

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