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.

Maxwell Equations Derived from Coulomb’ Law Mathematically vs. Maxwell-type Gravity Derived from Newton’s Law Mathematically

“…Recently, Faraday's law has been derived by curling the Lienard-Wiechert potential [1]. Ampere's law was derived from the Biot-Savart law [2].…”