The single four-dimensional tensor equation $\partial_\mu F^{\mu \nu}=\mu_0 K^\nu$ represents a powerful unification in physics, compactly encoding the two inhomogeneous Maxwell's equations. This equation relates the divergence of the electromagnetic field tensor $F^{\mu \nu}$ to the four-current density $K^\nu$ (using $\mu_0$ for unit consistency). Specifically, when expanded, the $\nu=0$ (time) component of this tensor equation yields Gauss's Law ( $\nabla \cdot E =\rho / \epsilon_0$ ), while the $\nu=j$ (spatial) components collectively reproduce the Ampère-Maxwell Law ( $\nabla \times B =\mu_0 J +\mu_0 \epsilon_0 \frac{\partial \overline{5}}{\partial t}$ ). This demonstrates the elegant and inherent consistency of electromagnetism with Special Relativity.
Tensor Equation Unification-L.mp4
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