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When we say condition of a vector field F being conservative is curl F=0,does it mean that F=F(r)?.I know normally it does not look so.Please,then site an example where F is not a function of r,but still curl F=0.
When we say condition of a vector field F being conservative is curl F=0,does it mean that F=F(r)?.I know normally it does not look so.Please,then site an example where F is not a function of r,but still curl F=0.
A picked a constant vector field as a simple counterexample. Any vector field that can be expressed as the gradient of a scalar function has zero curl.
For the latter, [itex]\vec F = \vec F(\vec v), \vec v = d\vec r/dt[/itex], the curl is zero since the partials of [itex]\vec F[/itex] with respect to components of [itex]\vec r[/itex] are zero. Drag in a constant density fluid satisfies these conditions, and is definitely not conservative.
StatMechGuy:I really did not understand:Drag in a constant density fluid satisfies these conditions, and is definitely not conservative.
I really dislike it when classes take the perspective that if the curl is zero, then it has to be conservative
Generally velocity/time dependent forcing fields are not conservative. I really dislike it when classes take the perspective that if the curl is zero, then it has to be conservative.
When we say condition of a vector field F being conservative is curl F=0,does it mean that F=F(r)?.I know normally it does not look so.Please,then site an example where F is not a function of r,but still curl F=0.