Maxwell-Ampere law

The Maxwell-Ampère law is the electrodynamic equivalent of Ampere’s law. It adds an additional time-varying term:

$$\nabla \times \vec{B}=\mu \vec{J}+\mu {ϵ}_0\frac{\partial \vec{E}}{\partial t}$$

The key implication of Maxwell-Ampère is the inverse intuition of Faraday’s law of induction, that a changing electric field induces a magnetic field.

This extra term is called the displacement current:

$${\vec{J}}_d={ϵ}_0\frac{\partial \vec{E}}{\partial t}$$