Irrotational Vector Field vs Conservative Vector Field
If F is either an irrotational vector field or a conservative vector field,in both cases,curl F =0. Therefore you think that both the irrotational and the conservative vector fields are same. But reality is something different. Curl F =0 is the necessary and the sufficient condition for F to be irrotational but it is not the necessary and sufficient condition for F to be conservative. The necessary and the sufficient condition for F to be conservative is that it must be equal to the gradient of a scalar point function generally called potential function.
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