A compass needle points 21.2 degree E of N outdoors. However, when it is placed

Question

A compass needle points 21.2 degree E of N outdoors. However, when it is placed 9.80cm to the east of a vertical wire inside a building, it points 52.7 degree E of N. What is the magnitude of the current in the wire? The Earth?s field there is 4.10 x 10^-5 T and is horizontal. Not yet correct, tries 1/6 Hint: If the wire is vertical, what is the direction of the B-field from the wire at the location of the compass? When the compass is inside, think about the components of the B-field that are coming from the wire and from the Earth. You know the angle of the compass needle when it is indoors, and this gives you some information about the relative sizes of the North and East components of the total B-field.

Explanation / Answer

B sin theta2 = Bearth sin theta1

B cos theta2 = Bearth cos theta1 - Bwire

When we divide the two equations, we get

tan theta2 = (Bearth sin theta1) / (Bearth cos theta1 - Bwire)

tan 52.7 = (4.10 * 10-5 * sin 21.2) / ((4.10 * 10-5) cos 21.2 - Bwire)

Bwire = 2.69 * 10-5 T

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Bwire = (mu / 4 pi) (2 I / r)

2.69 * 10-5 = (10-7 * 2 I / 0.098)

I = 13.18 A

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