# Ampère's Circuital Law **The [[line integral]] of a [[magnetic field]] around a closed curve is proportional to the enclosed electric current.** ![[Ampere'sCircuitalLaw.svg|330]] *The system described by Ampère's circuital law; the right-hand rule can be used to relate the direction of the magnetic field lines to the direction of the enclosed electric current* > [!NOTE] Ampère's Circuital Law > **Ampère's circuital law**, also known simply as **Ampère's law**, states that the [[line integral]] of a [[magnetic field]] around a closed curve is *proportional* to the *net electric current enclosed* by the curve. Ampère's circuital law is one of [[Maxwell's equations]] and can be expressed in integral and differential form, which are equivalent due to [[Stokes' theorem]]. > The *integral* form of **Ampère's circuital law** is > $\oint_{C}\mathbf{B}\cdot d\mathbf{s}=\mu_{0}I_{\text{enc}}$ > - $C$ - the *curve of integration* > - $\mathbf{B}$ - *[[Magnetic Field#The B-field|magnetic field density]]* or the *$\mathbf{B}$-field* > - $d\mathbf{s}$ - an *infinitesimal curve element* > - $\mu_{0}$ - the *[[List of Physical Constants#Vacuum permeability|vacuum permeability]]* > - $I_{\text{enc}}$ - the *enclosed current* > The *differential* form of **Ampère's circuital law** is > $\nabla\times\mathbf{B}=\mu_{0}\mathbf{J}$ > - $\nabla\times\mathbf{B}$ - the *[[curl]] of the magnetic field density* or the *$\mathbf{B}$-field* > - $\mu_{0}$ - the *vacuum permeability* > - $\mathbf{J}$ - *total current density*