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What is exactly a conservative field?

I know the mathematical definitions such as the existence of a scalar potential, the curl of the field equals 0 (irrotational), path independence etc.

But I still don't get a physical understanding of such a field.

What's the significance of identifying whether a field is conservative or not?

I know the gravitational field is a conservative field. But it seems to me that it is just a matter of terminology...

Please inspire me.

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# Conservative field

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