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.

中文翻译：

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均匀带电圆环的静电势

由于电荷连续分布而产生的静电势和/或静电场的计算是所有基于微积分的本科物理课程中广泛讨论的主题。最常见的方法是考虑具有均匀电荷分布的物体，并通过对所有不同电荷的贡献进行积分来获得感兴趣的数量。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种技术，至少对于计算相对简单的特殊点或对称方向而言。令人惊讶的是，文献中基本上没有均匀带电的环面（即环形盘）的情况。人们可能会推测，均匀带电的环面并不是很有趣，因为它毕竟是一个带有中心圆孔的均匀带电圆盘。然而，我们在这项工作中表明，均匀带电环产生的静电势具有比人们预期的更有趣的特征。均匀带电的环插在均匀带电的圆盘和环之间。然而，这项工作的结果表明，均匀带电的环具有这样的静电特征，基本上可以被视为环状。一旦出现孔，无论孔有多小，均匀带电的环带的静电势的环状特征就很明显。这个问题的解决使我们能够关注这个被忽视但非常有趣的静电学案例研究的教学方面。我们认为，均匀带电环及其静电特性的问题值得在所有涵盖电学和磁学的基于微积分的本科物理课程中进行更深入的处理。