BE 518 F2017 Homework 6 SOLNS.pdf

BE 518 F2017 Homework 6 SOLNS.pdf - Problem 1 Show that for...

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Unformatted text preview: Problem 1. Show that for any vector field A, Vx (VxA) =V(V-A)—V2A Hlnt: Prove it for the x com ponent and the others will follow from circular permutation of indices. Orb = 92” vaawflfir " 9K; m agz 9&2 0+L18V JIWANIOMI ppHaw L/ Cllrc ; 3K [I fermmffl'flcb c'f "Adi/“ar— Problem 2. Prove thisB identity for the scalar triple product: A- (B x C): B-(C x A) @ ghaw A (BKC>= 6 (6X12) // . A" @(ngcr' “€204“? (“CV “WWW 4;?ch : my: ; - Mac} + A; $sz ‘ 4;“ *MW‘W‘X = exfcgflr Mg) + 6%wa ‘CXA%>*@%<0‘42 ’ W“) = wax?) / Problem 3. Show that the curl of the gradient of any scalar field is zero. l\ (\ ’\ x 243’ ; 3K @ VX[7A am M2 m 5? Y; 72. \ J 274 W1 “ 22 ,914 ”(£13,324 \ «JP—f 553;) *Mam 91> *7? MK 933+ r 0 M A f; +w.‘ce, Cowh'wuomlj Wfiflévémfiltzé/e. Problem 4. Find an expression for the electric field of a plane wave with these properties: (0 it is linearly polarized. (ii) It propagates in a direction that makes equal angles to the x, y, and z axes, (iii) It has zero electric field in the x direction. A "0 ,.. a 1. 4 q 4 A (")E = Ea 005(IC'V‘W'6) I Ea = axx+€agj+Eflgi Ci") E I k()( +2, ‘1' f) Malta: Cfiual “ma {3; w/z ax“ «75 a l<== 4m 0 El! C/‘JC, Val/K211 4': LP WP Q: “,4! us. i lef ClL'Ow. ll EOX+Eag+Eae =- 0 (HI) E0X= 0 F5 E02: ’5"? 5— wow We we) Mule % 99hr w! yfz mice; Merlmm kangair’wle : 59 9min? liq. /,f3 is h malts, “(la ...
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