A high-voltage power line carries a current of 110Aat a location where the Earth

Question

A high-voltage power line carries a current of 110Aat a location where the Earth's magnetic field has a magnitude of 0.59 G and points to the north, 64 degrees below the horizontal.

1) Find the direction of the magnetic force exerted on a 290m length of wire if the current in the wire flows horizontally toward the east.

2) Find the magnitude of the magnetic force exerted on a 290m length of wire if the current in the wire flows horizontally toward the east.

3) Find the direction of the magnetic force exerted on a 290m length of wire if the current in the wire flows horizontally toward the south.

4)

Find the magnitude of the magnetic force exerted on a 290m length of wire if the current in the wire flows horizontally toward the south.

Explanation / Answer

Let's say the x-direction points east, the y-direction points north, and the z-direction points upward.

(force on wire) = (current)(length of wire) x (magnetic field)
F = iL x B ("x" denotes a cross product of vectors)

i = 110 A
L = <290 m, 0, 0>
B = <0, (0.59e-4)cos62

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