In this paper we present the analytical calculations to derive the magnetic field of a solenoid by solving exactly a fractional integral with the use of a novel method. Starting from the Biot-Savart law, we consider a coil of negligible thickness with a stationary electric current. We derive the expressions of the on- and off-axes magnetic field components. The results have been compared to some simplified and known analytical formulae as well as to a commercial numerical code showing a good agreement.

中文翻译：

---

螺线管磁场的一种新的精确解析表达式

在本文中，我们提出了通过使用一种新方法精确求解分数积分来推导螺线管磁场的分析计算。从 Biot-Savart 定律开始，我们考虑一个厚度可以忽略不计的线圈，其电流恒定。我们推导出轴上和离轴磁场分量的表达式。结果已与一些简化和已知的分析公式以及显示良好一致性的商业数字代码进行了比较。