I Irrotational vector and curl

  • Thread starter Apashanka
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If the curl of a vector is 0 e,g ##\vec \nabla×\vec A=0## the vector A is said to be irrotational,can anyone please tell how rotation is involved with ##curl## of a vector??
If you recall that curl is related to a line integral path about a point aka the Stokes theorem. Then if that integral is not zero then you have rotation.

One little mental picture is to place a paddlewheel at the point of interest and if it spins then there’s rotation.



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Point of order: A vector by itself cannot have a curl. The concept makes no sense. All differential operators you will encounter in vector analysis involve fields. In the case of the curl, a vector field.

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