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A conservative vector field is a vector field v with a zero curl:
∇ × v = 0Such vector fields can always be expressed as the gradient of a scalar field φ. This is usually defined as the negative of the scalar field:
v = -∇φThe scalar field thus defined is called the potential of the vector field.
If you're more confused than before, rest assured that vector calculus is one of the most hilarious branches of mathematics, even if it is partially derivative.
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