Linked from

The 14 pages that link to Curl, each with the reason it gives.

• Maxwell's equationsRelated: Faraday's law and the Ampère–Maxwell law relate field curls to changing fields and sources.

• Vector fieldRelated: It identifies where the field circulates around a point.

• GradientCompared with: Unlike the gradient, curl acts on vector fields and detects local rotation.

• DivergenceCompared with: Curl detects rotational behavior, whereas divergence detects net outward flow.

• LaplacianCompared with: Curl acts on vector fields and measures rotation, unlike the scalar Laplacian’s net curvature.

• Conservative forceRelated: In a simply connected region, a zero-curl force field is conservative.

• Stokes' theoremBroader topic: Stokes' theorem integrates this local rotation across the surface.

• Vector calculusBroader topic: It quantifies the field's tendency to circulate around a point.

• Exterior derivativeBroader topic: In three dimensions, the exterior derivative of a 1-form corresponds to the curl.

• Magnetic vector potentialBroader topic: Taking the curl of the potential produces the magnetic field.

• Conservative vector fieldRelated: A conservative field has zero curl wherever its potential is twice differentiable.

• Solenoidal vector fieldRelated: The divergence of every sufficiently smooth curl is zero, producing solenoidal fields.

• Helmholtz decompositionRelated: The divergence-free component is determined through its curl, together with boundary data.

• Gradient theoremRelated: In a simply connected domain, a curl-free field can be a gradient, linking this test to the theorem’s applicability.