Theoretical Derivation of Ampere's Circuital Law

Abstract

Amperes circuital law is a very important formula in classical electromagnetics. However, the corresponding detailed theoretical derivation is rarely seen in relevant textbooks. In this paper, based on the magnetic field produced by a moving charge, we taken the divergence theorem and rotation of the magnetic field, respectively, and given a series of mathematical transformations. At last, we derived Ampere's circuital law of the magnetic field, which is very helpful to understand the physical source of the law.