本文處理有關靜電學的問題：有一柱軸平行於z 方向的中空的無限長圓柱，當其柱面被給予一個與z 無關的任意的電位分布時，求其圓柱面內所有點的電位分布。因為問題中的所有物理量與z 無關，所以它 變成了二維的靜電學問題。我們分別用了傅立葉級數法和格林函數法來做理論分析，並獲得了相同的表達 式，證明兩種方法是等價的。然後我們給予表面兩種不同特定的電位分布，並將圓柱內各點電位實際計算 出來。過程中，還對反正切函數給予了較深刻的認識。

In this paper, we deal with the problem of electrostatics: there is a hollow infinite ling cylinder with a columnar axis parallel to the z direction. When the surface of the cylinder is given an arbitrary potential distribution independent of z, we solved the potential distribution at all points inside the cylinder. Because all the physical quantities in the problem are independent of z, it becomes a two-dimensional electrostatic problem. We use the Fourier series method and the Green’s function method to do the theoretical analysis, and obtain the same expression, which prove that the two methods are equivalent. Then we give two different specific potential distributions and work out the potential distribution. In the mean time, it make us having a more profound understanding about arctangent function.