Ex2Ch8

Ex2Ch8 - -2 z j + (3 y-1) k . (b) From Gauss theorem and...

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1 Review Example 2, Chapter 8. (a) Let F = ( x 2 + y - 4) i + 3 xy j + (2 xz + z 2 ) k . Calculate the divergence and curl of F . (b) Find the flux of the curl of F across the surface x 2 + y 2 + z 2 = 16 ,z 0 . (c) Find the flux of F across the surface of the unit cube [0 , 1] × [0 , 1] × [0 , 1] . Solution. (a) By a direct computation, ∇ · F = 7 x + 2 z, ∇ × F =
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Unformatted text preview: -2 z j + (3 y-1) k . (b) From Gauss theorem and the identity ( F ) = 0, we can conclude that the answer is 0. (c) Applying Gauss theorem once again, we get ZZ S F n dS = Z 1 Z 1 Z 1 7 x + 2 z dxdy dz = 9 2 ....
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