How to Test if a Vector Field is Conservative // Vector Calculus

A vector field is conservative if the line integral is independent of the choice of path between two fixed endpoints. We have previously seen this is equivalent of the Field being able to be written as the gradient of a scalar potential function. In this video we will derive a simple test to see whether a field is indeed conservative. We discover three equations that relate different partial derivatives of the components of the field, and if those equations are equal, then the field is conservative.

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