Ampere's Law

Topics

• Ampere’s Law in Matter

$\oint \vec{B}\cdot \mathrm{d}\vec{l}={\mu }_0\int \vec{J}\cdot \mathrm{d}\vec{A}$

• Integral form
• Can be derived from differential form using Stoke’s Theorem

$\nabla \times \vec{B}={\mu }_0\left(\vec{J}+{\epsilon }_0\frac{\partial \vec{E}}{\partial t}\right)$

• $\vec{B}$ is the magnetic field
• ${\mu }_0$ is the magnetic constant
• ${\epsilon }_0\frac{\partial \vec{E}}{\partial t}$ is called the Displacement Current

$\nabla \times \vec{B}={\mu }_0\vec{J}$

• In the static case