ece302hw3lastproblem - Verify Stokes’ 3 Theorem for the...

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Unformatted text preview: . Verify Stokes’ 3 Theorem for the vector field A: Recs 6 + 415 sin 6 by evaluating" 1t on the hemisphere of unit radius. Solution: ' A = Roose+¢sin6 = RAR+GA9 +$A¢. Hence, A3 = cos 6, A9 = O, Aq, = sine; VxAzii 1 (3(A¢Sine))1_ éii(mfi)_‘l§é£ Reine BR 312 R 88 . 1 _. RRsinG— 86 a(sir:2 B)— QR— 3R (Rsin6)— —¢R—— 36 3(case) =fi2cos6 _é5ine+¢.slllg_ R For the hemisphexical surface, d5 = RRZ sine d6 dd). 27:1:[2 f (V x A) ds ¢=o 9:0 ~~ 7:]2 A ' . ‘ =f2" [=0 (R2cosG_ 651116 , Tabs 11116) ~2RR sin6d6d¢ ¢=o R R 12:1 111/2 =4TER 5511129 =27t. 2 o R=1 The contour C is—the circle in the x—y plane bounding the hemispherical surface. 74A di: f: (Rc039+¢sin6)- -¢Rddp =Rsin6 fzndq) =2'm. G=1t/2 . 6.4!:2 R=/12 R=1 ...
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