15_R_9 - , e , 1 ) can be parametrized r ( t ) = e t i + e...

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9. F = ( x 2 / y ) i + y j + k . The field lines satisfy y dx x 2 = dy y = dz . Thus dx / x 2 = dy / y 2 and the field lines are given by 1 x = 1 y + C 1 , ln y = z + C 2 . The field line passes through ( 1 , 1 , 0 ) provided C 1 = 0 and C 2 = 0. In this case the field line also passes through ( e , e , 1 ) , and the segment from ( 1 , 1 , 0 ) to ( e
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Unformatted text preview: , e , 1 ) can be parametrized r ( t ) = e t i + e t j + t k , ( ≤ t ≤ 1 ). Then Z F • d r = Z 1 ( e 2 t + e 2 t + 1 ) dt = ( e 2 t + t ) ± ± ± 1 = e 2 ....
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This note was uploaded on 03/08/2012 for the course MATH 120 taught by Professor Onurfen during the Spring '12 term at Middle East Technical University.

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