div_1 - PHY2061 R. D. Field Divergence of a Vector Function...

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PHY2061 R. D. Field Department of Physics div_1.doc Univesity of Florida Divergence of a Vector Function Let z z y x F y z y x F x z y x F z y x F z y x ˆ ) , , ( ˆ ) . . ( ˆ ) , , ( ) , , ( + + = ! be a vector function of position. The divergence of a vector function is the flux out of a volume, V, per unit volume, in the limit of infinitesimal V. It is the surface integral per unit volume as the volume enclosed by the surface goes to zero: = = Surface Closed V A d F V F F div ! ! ! ! ! 1 lim ) ( 0 Symbols:
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