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Unformatted text preview: Physical application of divergence and divergence theorem Consider a vector field ~ J = ~ v , where is mass density and ~ v is a flow velocity The net change of mass in a time dt in a volume element is determined only by ~ J on the surface of dM dt = Z Z ~ J nd By the divegence theorem, we can change this to a volume integral dM dt = Z Z Z ~ Vd We also see that dM dt is related to the change in in the volume, so dM dt = Z Z Z d dt d Chapter7: Fourier series Continuity equation Setting these last equations equal, we get the continuity equation ~ J + t = 0 An example is diffusion where ~ J = D n , then D 2 n = n t We will encounter this simple equation more in later chapters Chapter7: Fourier series Gauss Law In Gauss Law, the vector field is ~ E and Z Z ~ E nd = Q We can use the divergence theorem to express the lefthand side as a volume integral of...
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This note was uploaded on 07/30/2011 for the course PHZ 3113 taught by Professor Staff during the Spring '03 term at University of Central Florida.
 Spring '03
 Staff

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