At a site where the Earth\'s magnetic field has a magnitude of 0.45 gauss (where

Question

At a site where the Earth's magnetic field has a magnitude of 0.45 gauss (where 1 gauss = 1.00 times 10^-4 T) and points to the north, 68degree below the horizontal, a high-voltage power line 207 m in length carries a current of 120 A. Determine the magnitude and direction of the magnetic force exerted on this wire, if the orientation of the wire and hence the current is as follows. horizontally toward the south What quantities determine the magnitude of the magnetic force acting on a current carrying wire in a magnetic field? N horizontally toward the west What quantities determine the magnitude of the magnetic force acting on a current carrying wire in a magnetic field? N

Explanation / Answer

B =0.45 G = 0.45*10^-4 T, l =207 m, i =120 A

(a) i = -120 j, B = 0.45*10^-4 j

F =l(ixB) = (207) [(-120j)x(0.45*10^-4*j )]

magnitude F = 0

direction 0 0 Below the horizontal

(b) i = -120 i

F =l(ixB) = (207) [(-120i)x(0.45*10^-4*j )]

F = (207)(120)(0.45*10^-4) k

magnitude F = 1.112 N

Direction =90-68 =22 0 measured below the horizontal

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