## Saturday, December 24, 2022

### What Are Maxwell's Original Twenty Equations?

James Clerk Maxwell's original 20 equations are a set of equations that describe the behavior of electric and magnetic fields, and how they interact with matter. These equations are considered to be some of the most important and fundamental equations in physics, and they form the foundation of classical electromagnetism. Original Maxwell equations were written using quaternions and potentials. Quaternions combine vector and scalar part. Electric and magnetic fields were defined as difference in potential. There were two kinds of potentials - electric and magnetic. Today's "Maxwell's" equations are actually Heaviside equations, which are limited edition of the original electromagnetic theory.

The 20 equations are:

Gauss's Law for Electric Fields
Gauss's Law for Magnetic Fields
Faraday's Law of Electromagnetic Induction
Ampere's Law
The Biot-Savart Law
The Lorentz Force Law
The Electric Field Intensity Equation
The Magnetic Field Intensity Equation
The Electric Flux Density Equation
The Magnetic Flux Density Equation
The Electric Displacement Field Equation
The Magnetic Vector Potential Equation
The Electric Scalar Potential Equation
The Magnetic Scalar Potential Equation
The Electric Charge Density Equation
The Electric Current Density Equation
The Continuity Equation for Electric Charge
The Continuity Equation for Electric Current
The Lorentz Transformations
The Wave Equation for Electromagnetic Waves

These equations describe a wide range of phenomena, including the behavior of electric and magnetic fields, the forces acting on charged particles in those fields, the generation and transmission of electromagnetic waves, and the relationship between electric and magnetic fields and the charges and currents that produce them. They are used in many areas of physics, including electromagnetism, electrical engineering, and particle physics, and have had a wide-ranging impact on our understanding of the physical world.