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Unformatted text preview: Physics 208, Assignment 5, Solutions, 2/21/09, RT Problem 1. (a) As figure (a) shows, the horizontal components of magnetic field can- cel at the point on the ground directly below the center of the power lines. The resulting field is straight down, parallel to the negative y-axis. 1 i =i 2 i =-i 1 i =-i B 1 2 B 2 B B 1 (a) d h =4m =12 m (b) x y x y r 2 i =i (=100 A) (b) Reversing both current directions reverses both fields and, therefore, also their resultant, which points straight up. (c) The angle and distance r satisfy sin = d/ 2 r , and r = radicalbig h 2 + ( d/ 2) 2 . The magnetic field at distance r from current i is i/ (2 r ). In case (a) the resultant of B 1 and B 2 is B y = 2 i 2 r sin = id 2 ( h 2 + ( d/ 2) 2 ) . You can check this formula against other formulas you know in special cases, such as h = 0 (wires on ground) or d = 0 , h negationslash = 0 in which case the currents cancel, giving no magnetic field. (d) | B y | = (4 10- 7 )(100)(4) 2 ( 12 2 + 2 2 ) = 5 . 4 10- 7 T . (e) As a fraction of the earths magnetic field this is | B y | B earth = 5 . 4 10- 7 . 5 10- 4 = 1 . 1 10- 2 . 1 As regards biological effects this would seem to make the power lines negligible. But one also has to worry whether or not oscillating fields are more serious than constant fields. Actually high frequency fields can be damaging. But 60Hz is such a small frequency that alternat- ing field effects are probably not very important....
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