A horizontal power line carries a current of 4530 A from south to north. Earth\'

Question

A horizontal power line carries a current of 4530 A from south to north. Earth's magnetic field (52.7 µT) is directed toward the north and is inclined downward at 54.0° to the horizontal. Find the (a) magnitude and (b) direction of the magnetic force on 130 m of the line due to Earth's field. A horizontal power line carries a current of 4530 A from south to north. Earth's magnetic field (52.7 µT) is directed toward the north and is inclined downward at 54.0° to the horizontal. Find the (a) magnitude and (b) direction of the magnetic force on 130 m of the line due to Earth's field.

Explanation / Answer

A.

B = Bx j + By k

B = B*cos 54 deg j - B*sin 54 deg k

L = 130 j

Force will be given by:

F = i*LxB

F = i*L*B*sin theta

F = 4530*130*52.7*10^-6*sin 54 deg

F = 25.11 N

Direction will be

Direction = LxB = jx(j - k) = jxj - jxk

Direction = 0 - i = -i = west direction.

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