Editing James Clerk Maxwell (section)

== Major Contributions ==

=== Maxwell's Equations ===

Maxwell's most famous contribution is the unification of previously separate laws of electricity and magnetism into a single coherent theory: **electromagnetism**.

The four fundamental equations he formulated are:

<math>
\begin{aligned}
&\text{(1) Gauss's Law:} && \nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0} \\
&\text{(2) Gauss's Law for Magnetism:} && \nabla \cdot \mathbf{B} = 0 \\
&\text{(3) Faraday's Law of Induction:} && \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t} \\
&\text{(4) Ampère-Maxwell Law:} && \nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \mu_0 \varepsilon_0 \frac{\partial \mathbf{E}}{\partial t}
\end{aligned}
</math>

These equations predict the existence of [[electromagnetic waves]], which travel through space at the speed of light:

<math>
c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}
</math>

This insight led to the conclusion that light is an electromagnetic wave, uniting optics with electromagnetism.

=== Kinetic Theory and Thermodynamics ===

Maxwell also made pioneering contributions to statistical mechanics and thermodynamics. He developed the [[Maxwell-Boltzmann distribution]], which describes the distribution of speeds among molecules in a gas.

<math>
f(v) = 4\pi \left( \frac{m}{2\pi k T} \right)^{3/2} v^2 e^{- \frac{mv^2}{2kT}}
</math>

Where:
* <math>v</math>: Speed of gas molecules
* <math>m</math>: Mass of a gas particle
* <math>k</math>: Boltzmann constant
* <math>T</math>: Absolute temperature

=== Maxwell's Demon ===

In a famous thought experiment, Maxwell introduced a hypothetical entity now known as '''Maxwell's Demon''' to explore the second law of thermodynamics. This idea continues to stimulate debates in physics regarding entropy and information theory.