Theoretical Derivation of Ampere's Circuital Law

Yiran Luo¹ and Shimeng Feng^2,

¹Shenzhen Senior High School, P.R. China

²School of Physics and Astronomy, Shanghai Jiao Tong University, P.R. China

Cite this paper:
Yiran Luo and Shimeng Feng. Theoretical Derivation of Ampere's Circuital Law. International Journal of Physics. 2020; 8(3):105-107. doi: 10.12691/ijp-8-3-3

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.

Keywords:
Ampere's circuital Law magnetic field electric field

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]	Su zengshu. Deduction of Ampere's loop law, Journal of Guangzhou University, 1987, 01: 130-133.
[2]	Rajaraman K. Ampere's Magnetic Circuital Law: A Simple and Rigorous Two-Step Proof [J]. International Journal of Electrical Engineering Education, 2001, Vol. 38 Issue 3, 38-43.
[3]	Nishmura H. From the Biot-Savart Law to Ampere's Magnetic Circuital Law via Synthetic Differential Geometry [J]. 2014, 87-89.
[4]	Wang Zaijun. Discussion on the application of Stokes formula and the curl of the magnetic field at the point on the infinite current carrying straight wire, College Physics, 2015(2): 20-24.
[5]	Zhao Haijun, Dai Jianfeng, Wang Daobin. Derivation of generalized Faraday's law and Ampere's loop law from Heisenberg equation Journal of Gansu science, 20129(4): 20-23.
[6]	Zhang Sanhui. College physics., electromagnetics. 1991. Volume 3 210-220.