In every beginning electricity and magnetism course, a good teacher usually insists that if one has an infinite charged plate or an infinity charged wire, one must first calculate the electric field to find the potential difference between two space points by making a linear integral of the field. One does it this way because of Coulomb's potential - i.e., the expression which allows for a direct calculation of the potential without first calculating the electric field - should not be used since these charge distributions are not bounded in space. Due to the unbounded nature of these distributions, Coulomb's potential diverges at all points of space in the two previously mentioned cases. However, we are going to demonstrate that in fact one can find the correct potential by properly removing the infinities that appear in the Coulomb's potential of these distributions. That is possible because electric potential, like potential energy, is only defined up to an additive constant, which in the mentioned cases can be chosen as an infinite constant. One can show that the removal of these infinities is a simple example of the renormalization techniques commonly used in Quantum Field Theory.

中文翻译：

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关于无界电荷分布的电位无穷大

在每一门刚开始的电学和磁学课程中，一位好老师通常都会坚持，如果一个人有一个无限带电的板或一根无限带电的电线，必须先计算电场，通过对两个空间点进行线性积分来求出两个空间点之间的电势差。场地。这样做是因为库仑势 - 即允许直接计算电势而不首先计算电场的表达式 - 不应该使用，因为这些电荷分布在空间中不受限制。由于这些分布的无界性质，在前面提到的两种情况下，库仑势在空间的所有点都是发散的。然而，我们将证明，事实上人们可以通过适当地去除库仑中出现的无穷大来找到正确的势能。这些分布的潜力。这是可能的，因为与势能一样，电势只能定义为一个加性常数，在上述情况下可以选择一个无穷大的常数。可以证明，去除这些无穷大是量子场论中常用的重整化技术的一个简单例子。