Curl measures the tendency of a field to circulate around a small loop.
WHAT HAPPENS IF…For F=(−2y,2x), what is curl?
Interactive exploration
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Connect the picture to the ideacurlzF=∂x∂Q−∂y∂P=c−b
For F=(by,cx), integrating F·dr around a counterclockwise radius-R circle gives (c−b)πR². Reversing traversal changes the circulation sign, but does not change the field’s curl. In F=(−ωy,ωx), angular speed is ω and curl is 2ω.
A detail that matters
A curved streamline alone does not establish nonzero curl.