A small compass is held horizontally, the center of its needle a distance of 0.1

Question

A small compass is held horizontally, the center of its needle a distance of 0.140 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 13.0 A, the needle points 34.0° east of north. (a) What direction does the current in the wire flow, toward or away from the earth's surface? (b) What is the magnitude of the horizontal component of the earth's magnetic field at the location of the compass?

Explanation / Answer

First Find B due to the wire at d = 0.14 m

Bwire = muzero I / (2 Pi d) = 2 x 10^-7 x 13 / 0.14 = answer T

now Tan theta = BhEarth / Bh wire because BhEarth is due north and Bhwire is East

so tan(90-34) = BhEarth/answer and find BhEarth

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