http://www.webassign.net/mi3/18-090-wire_compass_otherloc.jpg A wire is connecte

Question

http://www.webassign.net/mi3/18-090-wire_compass_otherloc.jpg

A wire is connected to batteries (not shown), and current flows through the wire. The wire lies flat on a table, and you are looking down on it from above. The wire is laid on top of a compass, resting about 6 mm above the needle. The distance d is 4.5 cm. The compass needle deflects 14 degrees from North, as shown. At this location the horizontal component of the Earth's magnetic field is 2e-5 tesla. What is the approximate magnitude of the magnetic field at location A, due to the current in the wire?

Explanation / Answer

magnetic field on the top of compass is B = Bo tan theta

B = 20 e -6 * tan 14

B = 4.98 e -6 Tesla

Now use this B = uoi/2pir

curent i = 4.98 e -6 * 2* 3.14 * 6 e -3/(4*3.14 e -7 )

current i = 0.1494 Amps

B field from each side of the wire at point A. Each side contributes:

here r = 4.5/2 = 2.25 cm oe 0.0225 m

B = 4*3.14 e -7 * 0.1474 /(2*3.14*0.0225)

B = 1.31 uT

Bnet due to Both sides = B1 +B2 = 1.31*2 = 2.62 uT

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