🎬Visualize Electric Field Divergence from Charge and Magnetic Field Curl from Changing Electric Field

The inhomogeneous Maxwell's equations define the source-dependent nature of the electromagnetic field, showing how fields are directly generated by physical entities. They are composed of two distinct source relationships: Gauss's Law ( $\nabla \cdot E \propto \rho$ ) illustrates that the static presence of charge ( $\rho$ ) is the fundamental source for the Divergence of the electric field, visualized by field lines visibly radiating outward from the central charge. The Ampère-Maxwell Law ( $\nabla \times B \propto J+\frac{\partial E}{\partial t}$ ) demonstrates that the source can be dynamic; here, a changing electric field ( $\partial E / \partial t$ ) acts as the source for the magnetic field's Curl, visualized by circulating magnetic vectors whose intensity and width are precisely synchronized with the instantaneous rate of change of the central electric field source.

Verifying the Inhomogeneous Maxwell's Equations in Spacetime | Proof and Derivationviadean on Notion