PHY2061 R. D. Field Department of Physics line_2.doc Univesity of Florida P1Closed LoopQuestion:When can the vector function),,(zyxFbe 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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