P30_062 - 62. We use B (x, y, z ) = (0 /4 )i s r/r3 , where...

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62. We use B ( x, y, z )=( µ 0 / 4 π ) i ±s × ± r/r 3 ,where∆ =∆ s ˆ jand ± r = x ˆ i+ y ˆ j+ z ± k .Thu s , ± B ( x, y, z )= ³ µ 0 4 π ´ i s ˆ j × ( x ± i + y ˆ z ± k ) ( x 2 + y 2 + z 2 ) 3 / 2 = µ 0 i s ( z ˆ i x ˆ k) 4 π ( x 2 + y s + z 2 ) 3 / 2 . (a) The feld on the z axis (at z =5 . 0 m) is ± B (0 , 0 , 5 . 0 m) = (4 π × 10 7 T · m / A)(2 . 0 A)(3 . 0 × 10 2 m)(5 . 0 m) ˆ i 4 π (0 2 +0 2 +(5 . 0 m) 2 ) 3 / 2 =2 . 4 × 10 10 T ˆ i . (b) ± B (0 , 6 . 0m , 0), since x = z =0. (c) The feld in the xy plane, at ( x, y )=(7 , 7), is ± B (7 . , 7 . , 0 (4 π × 10 7 T · m / A)(2 . 0 A)(3 . 0 × 10 2 m)( 7 . 0 m) ˆ k 4 π ((7 . 0 m) 2 +(7 . 0 m) 2 2 ) 3 / 2 =4 . 3 × 10 11 T ˆ k . (d) The feld in the
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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