Editing Curl (mathematics) (section)

==Inverse==

{{Main|Helmholtz decomposition}}

In the case where the divergence of a vector field {{math|'''V'''}} is zero, a vector field {{math|'''W'''}} exists such that {{math|1='''V''' = curl('''W''')}}.{{citation needed|date=April 2020}} This is why the [[magnetic field]], characterized by zero divergence, can be expressed as the curl of a [[magnetic vector potential]].

If {{math|'''W'''}} is a vector field with {{math|1=curl('''W''') = '''V'''}}, then adding any gradient vector field {{math|grad(''f'')}} to {{math|'''W'''}} will result in another vector field {{math|'''W''' + grad(''f'')}} such that {{math|1=curl('''W''' + grad(''f'')) = '''V'''}} as well. This can be summarized by saying that the inverse curl of a three-dimensional vector field can be obtained up to an unknown [[irrotational field]] with the [[Biot–Savart law]].