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HW9_sol

# 31 1 1 jlok ii z so x ii r but z v a at 0 prob 162

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Unformatted text preview: e V x B = 0 (B is uniform) and = -x' x + (y - y') - z' B)] dx' + dy' y; ProblemA 5.31 1 1 J.LoK ii = z; so x ii r)]. But z V (a) At 0 (Prob. 1.62). X x A Y -2V x (r =x 0, Bbelow[(B.J.LonI - =(r. V)B + r(V.s; B) -KB(V. = - K Z. x r = the surface of the solenoid, Babove V = B) = -2 = V)r z Evidently Eq. 5.74~holds.dx' ,( 0 = (-z' dy') X + (z' dx') y + [(y - y') dx' + x' dy'] z. dl' X = dy' (r. (b) In = 0 5.67, Vboth expressions B -z' uniform), and V . r = ~~ at the + ~: = so+Eq.+ 5.75 is satisfied. V)B Eq. and . B = 0(y - y') reduce to (J.LoR2VJa/3)sin()(iJ + ~~ surface, 1 1 1 = 3. Finally, (since is -x' aA 2Sin () ;., J.LoR4VJa 2J.LoRv.Ja . J.LoRv.Ja. () ;., 8 h I f .d 8A . () ;., f dx' x' - :y (B.V)r = (Bx 3:xdB1=--=-+dl' x:z) =Pol (-z' 3 dy') sm+Bx x+Byy+Bz =-z = B. Sosm dy'] = 0 tee + By~Pol Bz'P~ (xx+yy+zz) X 'P;!:I ury + [(y y') 3 + VxA'P' Z -~(B-3B) t S1 e B. = (z' dx') R=0 r R+ = r R qed 471" 1-3 [(x')2 r) = y')2 + (z')2]3/2 Eq. 5.76 is -J.LoRVJa sin() (iJ. Meanwhile 471" = av = a(~ x + (y - aVJRsi...
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