In vector calculus a conservative vector field is a vector field which is the gradient of a function, known in this context as a scalar potential. Conservative vector fields have the property that the line integral from one point to another is independent of the choice of path connecting the two points: it is path independent. Conversely, path independence is equivalent to the vector field being conservative. Conservative vector fields are also irrotational, meaning that (in three-dimensions) they have vanishing curl. In fact, an irrotational vector field is necessarily conservative provided that a certain condition on the geometry of the domain holds: it must be simply connected.
An irrotational vector field which is also solenoidal is called a Laplacian vector field because it is the gradient of a solution of Laplace's equation.
Read more about Conservative Vector Field: Definition, Path Independence, Irrotational Vector Fields, Irrotational Flows, Conservative Forces
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