Maxwell's Fourth Equation: the Ampere's Law

Authors

Ashanthi Maxworth PhD, University of Southern MaineFollow

Files

Description

The original Ampere's Law indicated the total magnetic field intensity along a closed loop is equal to the current enclosed. It was Dr. James Clerk Maxwell who introduced the missing term which was the rate of change of electric flux which is also known as the displacement current. As shown in the video of Faraday's Law and the Point form of Maxwell's Equations, the full Ampere's Law says the total magnetic flux along a losed loop is equal to the conduction and displacement currents. In this video Dr. Maxworth uses the original Ampere's Law to derive the inductance of a coaxial cable. The displacement current introduced by Maxwell, showed that a time varying electric field can create a time-varying magnetic field. Combining all of these four equations, comes the electromangetic fields, where a time-varying electric field creates a time-varying magnetic field, and in-turn a time-varying magnetic field creates a time-varying electric field, overall creating a propagating electromagnetic field. In the worksheet, you can observe different modes of a propagating electromagnetic fields inside a rectangular waveguide.

ISBN

978-3-031-73784-8 Published: 23 October 2024

Publication Date

1-2025

Keywords

Ampere's Law, Maxwell's Contribution, rate of change of electric flux, solenoids, magnetic field intensity

Disciplines

Electrical and Electronics | Engineering | Engineering Education

Comments

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

Recommended Citation

Maxworth, Ashanthi PhD, "Maxwell's Fourth Equation: the Ampere's Law" (2025). EM Fields With Prof. Maxworth. 1.
https://digitalcommons.usm.maine.edu/oer_engineering_maxworth_emfields/1