# Maxwell’s equations

In equations, Maxwell’s equations are []

Overview
The following are the four condensed Maxwell equations:

 Equation Formulator Name $\nabla \cdot \mathbf{D} = \rho$ Carl Gauss; Maxwell $\nabla \cdot \mathbf{B} = 0$ Carl Gauss; Maxwell $\nabla \times E = -\frac{\partial B}{\partial t}$ Michael Faraday; Maxwell $\nabla \times \mathbf{H} = \frac{\partial \mathbf{D}} {\partial t} + \mathbf{J}$ Andre Ampere; Maxwell

where D is the displacement current, E is the electric field, B is the magnetic flux density, H is the magnetic field strength, ρ is the free charge density, and J is the free current density.

In 2004, American science historian Robert Crease, stimulated by Graham Farmelo’s 2002 eleven equation list, wrote an article in Physics World entitled “The Greatest Equations Ever” in which he asked readers to send in their shortlists of great equations, explaining why their nominations belonged on the list and why, after which he received about 120 responses, proposing about 50 different equations. [1] The poll results were published in a followup article, which showed Maxwell's equations and the Euler equation topped the poll. The top 20 greatest equations are show below, listed in order of the number of people who proposed them: first two received about 20 mentions each out of a total of about 120; the rest received between two and 10 each. [2]

Quotes
The following are related quotes:

“Was it a god that wrote these signs, revealing the hidden and mysterious forces of nature around me, which fill my heart with quiet joy?”
Ludwig Boltzmann (1893), commentary (Ѻ) on Maxwell’s equations; inspired by opening monologue of Goethe’s Faust

“I saw that it was great, greater and greatest, with prodigious possibilities in its power. I was determined to master the book and set to work … It took me several years before I could understand as much as I possibly could. Then I set Maxwell aside and followed my own course. And I progressed much more quickly”
— Oliver Heaviside (1918), person who condense Maxwell’s equations with 20 variables down to just two equations in two variables

References
1. (a) Farmelo, Graham. (2002). It Must Be Beautiful: Great Equations of Modern Science. Granta Books.
(b) Crease, Robert P. (2004). “The Greatest Equations Ever: What Makes a Great Equation? Robert Crease seeks your Candidates and Criteria”, Physics World, May 10.
2. (a) Crease, Robert P. (2004). “The Greatest Equations Ever: Maxwell’s equations of Electromagnetism and Euler equation top a Poll to find the Greatest Equations of All Time” (abstract), Physics World, pgs. 14-15, Oct.
(b) Crease, Robert P. (2008). The Great Equations: Breakthroughs in Science from Pythagoras to Heisenberg. W.W. Norton & Co.