PHY2061 R. D. Field Department of Physics line_2.doc Univesity of Florida P1Closed LoopQuestion:When can the vector function),,(zyxF!be written as the gradient of a scalar function f(x,y,z)? We know that ∫⋅∇=−21)()(12PPrdfPfPf!!. This implies that ∫=⋅∇=−LoodClosedrdfPfPf0)()(11!!. Thus if we demand that fF∇=!!, then ∫=⋅LoopClosedAnyrdF0!!. But Stokes’ Theorem tell us that
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