Definition 1.1.1 The SI unit system is the most popular system of units that uses the fundamental units of seconds, meters, kilograms, ampere and Kelvin to derive a system of units to describe the universe.
Definition 1.1.2 A second (s) is the SI unit of time that is exactly 9192631770 hyperfine transitions of a Caesium-133 atom.
Definition 1.1.3 A meter (m) is the SI unit of distance that is exactly the distance light travels in $1/299792458$ seconds.
Definition 1.1.4 A kilogram (kg) is the SI unit of mass defined exactly by fixing Plank's constant $h=6.62607015 \times 10^{−34}\text{kg } \text{m}^2\text{s}^{−1}$.
Definition 1.1.5 An ampere (A) is the SI unit of current that is exactly the flow of $10^{19}/1.602176634$ protons per second.
Definition 1.1.6 A Kelvin (K) is the SI unit of absolute temperature defined exactly by fixing Boltzmann's constant $k=1.380649\times 10^{-23}\text{kg }\text{m}^2 \text{s}^{-2}\text{K}^{-1}$.
Definition 1.1.7 A Coulomb (C) is the SI unit of charge defined by $\text{C} = \text{A s}$ or exactly $10^{19}/1.602176634$ protons.
Definition 1.1.8 A Newton (N) is the SI unit of force defined by $\text{N} = \text{kg m}/\text{s}^{2}$.
Definition 1.1.9 A Joule (J) is the SI unit of energy defined by $\text{J} = \text{N m} = \text{kg }\text{m}^{2}/\text{s}^{2}$.
Definition 1.1.10 A Watt (w) is the SI unit of power defined by $\text{w} = \text{J}/\text{s}$.
Definition 1.1.11 A Pascal (Pa) is the SI unit of pressure defined by $\text{Pa}=\text{N}/\text{m}^2 = \text{J}/\text{m}^3 = \text{kg }\text{m}^{-1}\text{s}^{-2}$.
Definition 1.1.12 A Volt (V) is the SI unit of electric potential defined by $\text{V} = \text{J}/\text{C} = \text{w}/\text{A} = \text{kg }\text{m}^2\text{s}^{-3}\text{A}^{-1}$.
Definition 1.1.13 A Volt per Meter (V/m) is the SI unit of electric field defined by $\text{V}/\text{m} = \text{N}/\text{C} = \text{kg m}\text{s}^{-2}\text{A}^{-1}$.
Definition 1.1.14 A Telsa (T) is the SI unit of magnetic field defined by $\text{T} = \text{V s}/\text{m}^2 = \text{kg }\text{s}^{-2}\text{A}^{-1}$.
Definition 1.1.15 The fine structure constant denoted $\alpha$ is a dimensionless experimentally determined constant defined below. In any system of units, the fine structure constant is dimensionless and therefore has the same value1:
\[\alpha = \frac{\mu_0 e^2 c}{2 h} = \frac{e^2}{2\varepsilon_0 h c} \approx 0.0072973525643 \approx 1/137.035999177\]
Law 1.1.16 Maxwell's Equations are a set of coupled differential equations that form the foundations of classical electromagnetism.
\[\nabla\cdot \vec{E} = \frac{\rho}{\varepsilon_0}\]\[\nabla\cdot \vec{B} = 0\]\[\nabla\times\vec{E} = -\frac{\partial \vec{B}}{\partial t}\]\[\nabla\times \vec{B} = \mu_0\left( \vec{J} + \varepsilon_0\frac{\partial \vec{E}}{\partial t} \right)\]
Definition 1.1.17 The vacuum permittivity $\varepsilon_0$ is the physical constant defined in terms of the fine structure constant $\alpha$, charge of an electron $e$, Plank constant $h$ and speed of light $c$.
\[\varepsilon_0 = \frac{e^2}{2\alpha hc}\]
Definition 1.1.18 The vacuum permeability $\mu_0$ is the physical constant defined in terms of the fine structure constant $\alpha$, charge of an electron $e$, Plank constant $h$ and speed of light $c$.
\[\mu_0 = \frac{2\alpha h}{e^2c}\]
Result 1.1.19 The product of vacuum permittivity and vacuum permeability is the reciprocal of the speed of light squared.
\[\varepsilon_0\mu_0 = \frac{1}{c^2}\]
Definition 1.2 The Gaussian unit system is an alternate systems of units that uses the fundamental units of centimeters, grams, seconds and Kelvin to derive a system of units to describe the universe.
Definition 1.3 A second (s) is the SI unit of time that is exactly 9192631770 hyperfine transitions of a Caesium-133 atom.
Definition 1.4 A centimeter (cm) is the Gaussian unit of distance that is exactly the distance light travels in $1/29979245800$ seconds.
Definition 1.5 A gram (g) is the Gaussian unit of mass defined exactly by fixing Plank's constant $h=6.62607015 \times 10^{−27}\text{g } \text{cm}^2\text{s}^{−1}$.
Definition 1.6 A statcoulomb (statC) is the Gaussian unit of charge defined by $\text{statC} = \text{g}^{1/2}\text{cm}^{1/2}/\text{s}$ or exactly the amount of charge that results in one $\text{dyn}$ of repulsion between two particles of that charge separated by one $\text{cm}$.
Corollary 1.7 The vacuum permitivity in Gaussian units denoted $\varepsilon_0$ is unitless and $\varepsilon_0 = \frac{1}{4\pi}$.
Corollary 1.8 The vacuum permeability in Gaussian units denoted $\mu_0$ is unitless and $\mu_0=4\pi/c^2$.
Definition 1.9 The fine structure constant denoted $\alpha$ is a dimensionless experimentally determined constant defined below. In any system of units, the fine structure constant is dimensionless and therefore has the same value1:
\[\alpha = \frac{\mu_0 e^2 c}{2 h} = \frac{e^2}{2\varepsilon_0 h c} \approx 0.0072973525643 \approx 1/137.035999177\]
Result 1.10 Maxwell's equations in Gaussian Units are a set of coupled differential equations that form the foundations of classical electromagnetism.
\[\nabla\cdot\vec{E} = 4\pi \rho\]\[\nabla\cdot\vec{B} = 0\]\[\nabla\times\vec{E} = -\frac{1}{c} \frac{\partial \vec{B}}{\partial t}\]\[\nabla\times\vec{B} = \frac{1}{c}\frac{\partial \vec{E}}{\partial t} + \frac{4\pi}{c}\vec{J}\]