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Unformatted text preview: Section 13.7 wrapup: Go through Stewarts derivation of the formula S F d S = S F n dS = D F ( r u r v ) dA on page 781. Discuss Group Work 2: 1. G / x , G / y , G / z = 2 x ,2 y ,2 z 2. Outward 3. n = (1/ R ) x , y , z (check:  n  2 = (1/ R 2 ) ( x 2 + y 2 + z 2 ) = 1) 4. Everywhere but (0,0,0) 5. On the surface x 2 + y 2 + z 2 = R 2 , we have F = ( x i + y j + z k )/ R 3 = (1/ R 3 ) x , y , z so F n = (1/ R 4 ) ( x 2 + y 2 + z 2 ) = 1/ R 2 and S F n dS = S 1/ R 2 dS = (1/ R 2 ) Area( S ) = (1/ R 2 ) (4 R 2 ) = 4 . Check this with spherical coordinates: Imitating Example 4, we use r ( , ) = R sin cos i + R sin sin j + R cos k with 0 and 0 2 ; note that the extra factor of R will multiply r and r by R, so that r r = R 2 (sin 2 cos i + sin 2 sin j + sin cos k ) while F ( r ( ,...
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 Fall '11
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