Electrostatic potential of a uniformly charged annulus

IF 0.6 4区 教育学 Q4 EDUCATION, SCIENTIFIC DISCIPLINES
Orion Ciftja, Cleo L Bentley Jr
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Abstract

The calculation of the electrostatic potential and/or electrostatic field due to a continuous distribution of charge is a well-covered topic in all calculus-based undergraduate physics courses. The most common approach is to consider bodies with uniform charge distribution and obtain the quantity of interest by integrating over the contributions from all the differential charges. The examples of a uniformly charged disk and ring are prominent in many physics textbooks since they illustrate well this technique at least for special points or directions of symmetry where the calculations are relatively simple. Surprisingly, the case of a uniformly charged annulus, namely, an annular disk, is largely absent from the literature. One might speculate that a uniformly charged annulus is not extremely interesting since after all, it is a uniformly charged disk with a central circular hole. However, we show in this work that the electrostatic potential created by a uniformly charged annulus has features that are much more interesting than one might have expected. A uniformly charged annulus interpolates between a uniformly charged disk and ring. However, the results of this work suggest that a uniformly charged annulus has such electrostatic features that may be essentially viewed as ring-like. The ring-like characteristics of the electrostatic potential of a uniformly charged annulus are evident as soon as a hole is present no matter how small the hole might be. The solution of this problem allows us to draw attention to the pedagogical aspects of this overlooked, but very interesting case study in electrostatics. In our opinion, the problem of a uniformly charged annulus and its electrostatic properties deserves to be treated at more depth in all calculus-based undergraduate physics courses covering electricity and magnetism.
均匀带电环面的静电势
计算电荷连续分布所产生的静电势和/或静电场是所有微积分本科物理课程中都会涉及到的内容。最常见的方法是考虑具有均匀电荷分布的物体,并通过对所有微分电荷的贡献进行积分来获得感兴趣的量。均匀带电的圆盘和环的例子在许多物理教科书中都很突出,因为它们很好地说明了这一技术,至少对于特殊点或对称方向,计算相对简单。令人惊讶的是,文献中基本上没有关于均匀带电的环面,即环形盘的例子。人们可能会猜测,均匀带电的环面并不十分有趣,因为它毕竟是一个带有中心圆孔的均匀带电圆盘。然而,我们在这项研究中表明,均匀带电环面所产生的静电势具有比人们想象的要有趣得多的特点。均匀带电的环形体介于均匀带电的圆盘和环形体之间。然而,这项工作的结果表明,均匀带电的环状体所具有的静电特征基本上可以被看作是环状的。一旦出现孔洞,无论孔洞有多小,均匀带电环面静电势的环状特征都会显现出来。通过解决这个问题,我们可以关注这个被忽视但却非常有趣的静电学案例研究的教学方面。我们认为,在所有以微积分为基础、涵盖电学和磁学的本科物理课程中,都应该更深入地讨论均匀带电环面及其静电特性问题。
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来源期刊
European Journal of Physics
European Journal of Physics 物理-物理:综合
CiteScore
1.70
自引率
28.60%
发文量
128
审稿时长
3-8 weeks
期刊介绍: European Journal of Physics is a journal of the European Physical Society and its primary mission is to assist in maintaining and improving the standard of taught physics in universities and other institutes of higher education. Authors submitting articles must indicate the usefulness of their material to physics education and make clear the level of readership (undergraduate or graduate) for which the article is intended. Submissions that omit this information or which, in the publisher''s opinion, do not contribute to the above mission will not be considered for publication. To this end, we welcome articles that provide original insights and aim to enhance learning in one or more areas of physics. They should normally include at least one of the following: Explanations of how contemporary research can inform the understanding of physics at university level: for example, a survey of a research field at a level accessible to students, explaining how it illustrates some general principles. Original insights into the derivation of results. These should be of some general interest, consisting of more than corrections to textbooks. Descriptions of novel laboratory exercises illustrating new techniques of general interest. Those based on relatively inexpensive equipment are especially welcome. Articles of a scholarly or reflective nature that are aimed to be of interest to, and at a level appropriate for, physics students or recent graduates. Descriptions of successful and original student projects, experimental, theoretical or computational. Discussions of the history, philosophy and epistemology of physics, at a level accessible to physics students and teachers. Reports of new developments in physics curricula and the techniques for teaching physics. Physics Education Research reports: articles that provide original experimental and/or theoretical research contributions that directly relate to the teaching and learning of university-level physics.
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