Ampere-Maxwell Law

Differential Form

$$\nabla\times\mathbf B =\mu_0\mathbf J+\mu_0\varepsilon_0\frac{\partial\mathbf E}{\partial t}.$$

Displacement Current

The term

$$\mu_0\varepsilon_0\frac{\partial\mathbf E}{\partial t}$$

is Maxwell’s correction. It makes charge conservation compatible with the field equations and permits electromagnetic waves.