So lets say we have the vector field x^2yi+xy^2j, obviously the field is not conservative since dq/dx-dp/dy=y^2-x^2=/=0(adsbygoogle = window.adsbygoogle || []).push({});

however, lets say we wanted to find where locally the field would behave like a potential field, so we set y^2-x^2=0, so y=x (along the y=x line the field behaves like a conservative field). So my question is, a) is this true? b) is there some way to get an approximate scalar field whose gradiant behaves like the vector field locally along the y=x line?

Just something I was pondering.

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# Green's Theorem and Conservative Fields

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