James Clerk Maxwell

James Clerk Maxwell connected changing electrical and magnetic phenomena in a common field description. The displacement current makes that description compatible with charge conservation. In modern SI notation, taking the divergence of $\nabla \times \mathbf{H}=\mathbf{J}+{\partial }_t\mathbf{D}$ and using $\nabla \cdot \mathbf{D}=\rho$ gives $\nabla \cdot \mathbf{J}+{\partial }_t\rho =0$. The correction therefore has a concrete purpose when charge is accumulating, as in a charging capacitor. His treatise develops the general field equations and their connection with circuits and electromagnetic induction.^[ref]

James Clerk Maxwell (1831–1879) was a Scottish physicist and mathematician renowned for his groundbreaking contributions to the fields of electromagnetism, thermodynamics, and kinetic theory. He is perhaps best known for formulating Maxwell's equations, which describe the behavior of electric and magnetic fields and their interactions with matter. These equations unified the previously separate fields of electricity and magnetism into a single coherent theory known as electromagnetism.