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Curl as its name imply means the vector filed move in
a circular way. In other words the vector form a
circular closed form. The value of the rotor is the
magnitude of the rotation and the direction of the
vector curl-rotor is the axis of rotation.
But also means something else, a non zero curl vector
means the vector field will not have a "source" and
"sink" as oppose to static electric filed for example.
In other words, taken as example the magnetic
filed(B or H) the vector fields will always have
closed curve, there will be no "independent" poles
or source/sink and the fields will close to path.