Physlib.Electromagnetism.Basic

The charge density is a function that maps a time $t$ and a position in space $\mathbf{x}$ to a real number, typically denoted as $\rho(t, \mathbf{x}) \in \mathbb{R}$.

The current density is defined as a function that maps a time $t \in \text{Time}$ and a position $x \in \text{Space}$ to a vector in the 3-dimensional Euclidean space $\mathbb{R}^3$. This represents the vector field of electric current flow per unit area at a specific time and spatial coordinate.

The speed of light $c$ is defined as the reciprocal of the square root of the product of the vacuum permeability $\mu_0$ and the vacuum permittivity $\epsilon_0$ of the electromagnetic system $\mathcal{E}$: $$c = \frac{1}{\sqrt{\mu_0 \epsilon_0}}$$

Coulomb's constant $k_e$ for an electromagnetic system $\mathcal{E}$ is defined as the real number: $$k_e = \frac{1}{4\pi\epsilon_0}$$ where $\pi$ is the mathematical constant pi and $\epsilon_0$ is the vacuum permittivity associated with the system $\mathcal{E}$.