物理与工程

建立清晰牢固的物理概念，以简洁的形式解决物理问题，是物理教学的基本目的。本文以求均匀带电无限长直导线的电势为例，按照《电磁场与电磁波》教材的体例，由Helmholtz定理引入电势，由单位正电荷在电场作用下所做的功引出电势的定义式，通过对有限大和无限大带电体电场的讨论，说明从电势的定义出发，便不会出现病态的数学定义，能够解决因套用有限大带电体的电势公式所致的发散积分问题。无限大带电体是简单化、理想化和相对化的结果，故不能像有限大带电体那样选无限远处为电势参考点，而是要选有限远处为参考点。选定参考点后，有限和无限大带电体的电势如同电势差一样都是可以测量的。

Establishing clear and solid physical concepts and solving physical problems in a concise form are the fundamental objectives of physics teaching. This paper takes the calculation of the electric potential of a uniformly charged infinite long straight wire as an example. Following the format of the textbook on “Electromagnetic Fields and Waves, ” it introduces the electric potential through Helmholtz's theorem and derives the definition of electric potential based on the work done by a unit positive charge in an electric field. By discussing the electric fields of both finite and infinite charged bodies, it demonstrates that starting from the definition of electric potential avoids pathological mathematical definitions and can resolve the issue of divergent integrals caused by the misuse of the electric potential formula for finite charged bodies. Infinite charged bodies are the result of simplification, idealization, and relativization, and thus, they cannot have their electric potential reference points selected at infinity like finite charged bodies. Instead, a finite distance must be chosen as the reference point. Once the reference point is determined, the electric potential of both finite and infinite charged bodies, like potential difference, becomes measurable.