A conservative vector field is defined as being the gradient of a function, or as a scaler potential. Conservative vector fields are not dependent on the path; they are path independent. Conversely, the path independence of the vector field is measured by how conservative it is. These fields are also characterized as being irrotational, which means they have vanishing curls. Actually, irrotational vector fields are conservative as long as a certain condition on the geometry of the domain is true: there must be a simple connection.
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