A segment of a high-voltage power line is 250 m long and carries 110 A current.

Question

A segment of a high-voltage power line is 250 m long and carries 110 A current. At this particular location, Earth's magnetic field is directed toward the North, at an angle of 72 degrees below horizontal (i.e., downward into the ground at an angle). The field is uniform and has a magnitude of 0.59 Gauss. If current in the power line is flowing horizontally toward the east, what is the magnitude of the magnetic force on the wire? If the current is flowing horizontally toward the south, what is the magnitude of the magnetic force on the wire?

Units: 1 Gauss is equal to 10-4 T.

Please draw a diagram showing the angle between current direction and magnetic field direction. I know to use the formula F=ILBsin(theta) but I am having trouble visualizing this problem.

Explanation / Answer

I can understand your problem, let;s find the component of magnetic field along north direction = B cos 72

F = Bcos72 ( I ) L sin 90 = (0.59 x 10^-4) (110) (250) cos 72= 5.01 N apprx

If the current is flowing south, we will consider Bsin 72 component of mangetic filed

F = Bsin 72 (I) L sin 90 = (0.59 x 10^-4) (110) (250) sin 72=1.543 N apprx

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