line_2 - PHY2061 R. D. Field Question: ! F ( x, y, z ) be...

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PHY2061 R. D. Field Department of Physics line_2.doc Univesity of Florida P 1 Closed Loop Question: When can the vector function ) , , ( z y x F ! be written as the gradient of a scalar function f(x,y,z) ? We know that = 2 1 ) ( ) ( 1 2 P P r d f P f P f ! ! . This implies that = = Lood Closed r d f P f P f 0 ) ( ) ( 1 1 ! ! . Thus if we demand that f F = ! ! , then = Loop Closed Any r d F 0 ! ! . But Stokes’ Theorem tell us that
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