Understanding Gauss's Law
This is part of a Series on Understanding Maxwell's Equations
Maxwell’s equations describe the dynamics of the electric and magnetic fields. At the end of this series we will set the charge equal to zero and derive a wave equation that happens to travel at the speed of light. That wave turns out to be actual light!
Gauss’ Law: $$\nabla \cdot \boldsymbol{E} = 4 \pi \rho$$
To understand this, let’s start with \( \boldsymbol{E} \), the electric field. The electric field is a function that attaches an electric force vector to every point in space:
$$\boldsymbol{E} : \mathbb{R}^3 \to \mathbb{R^3}$$
Another way to think about this is if you have a coordinate system and the point \((x,y,z)\), then \(\boldsymbol{E}(x,y,z)\) is the electric force vector at that point in space
Backlink: Time in Physics