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A horizontal compass is placed 17 cm due south from a straight vertical wire carrying a...

A horizontal compass is placed 17 cm due south from a straight vertical wire carrying a 46 A current downward. In what direction does the compass needle point at this location? Assume the horizontal component of the Earths field at this point is 0.45 x 10-4 T and the magnetic declination is 00. 48. X。(counterclockwise from east is positive)

A horizontal compass is placed 17 cm due south from a straight vertical wire carrying a 46 A current downward. In what direction does the compass needle point at this location? Assume the horizontal component of the Earth's field at this point is 0.45 x 10-4 T and the magnetic declination is 00. 48. X。(counterclockwise from east is positive)
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Answer #1

B = mu0 I / 2 pi r

B = (4 pi * 10-7 * 46) / (2 pi * 0.17) = 5.41 * 10-5 T

Bnet = sqrt [(5.41 * 10-5)2 + (0.45 * 10-4)2]

Bnet = 7.04 * 10-5 T

theta = tan-1 [0.45 * 10-4 / 5.41 * 10-5]

theta = 39.7 deg

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