A small compass is held horizontally, the center of its needle a distance of 0.2

Question

A small compass is held horizontally, the center of its needle a distance of 0.240 m directly north of a long wire that is perpendicular to the earth's surface. When there is no current in the wire, the compass needle points due north, which is the direction of the horizontal component of the earth's magnetic field at that location. This component is parallel to the earth's surface. When the current in the wire is 38.0 A, the needle points 11.0° east of north. (a) What direction does the current in the wire flow, 1 - toward or 2 - away from the earth's surface? Give the number of the correct answer. (b) What is the magnitude of the horizontal component of the earth's magnetic field at the location of the compass?

Explanation / Answer

A) current is flowing towards the earth's surface.

B) First Find B due to the wire at d = 0.24 m

Bwire = u0I/(2Pi*d) = 2 x 10-7 x 38 / 0.24 = 3.1667 x 10-5 T

now tan(theta) = Bh(Earth) / Bh(wire) because Bh(Earth) is due north and Bh(wire) is East

so tan(79) = Bh(Earth)/3.1667 x 10-5

Bh(Earth) = 1.63 x 10-4 T

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