A long current-carrying wire, oriented North-South, lies on a table (it is conne

Question

A long current-carrying wire, oriented North-South, lies on a table (it is connected to batteries which are not shown). A compass lies on top of the wire, with the compass needle about 3 mm above the wire. With the current running, the compass deflects 17 degrees to the West. At this location, the horizontal component of the Earth's magnetic field is about 2e-5 tesla.

What is the magnitude of the magnetic field at location A, on the table top, a distance 2.9 cm to the East of the wire, due only to the current in the wire?

Explanation / Answer

You have Bearth and you know Bnet so make a right triangle to find Bwire.
Bwire = tan(17)*2e-5 = 6.116*e-6

You first have to use the approximation of the magnetic field of a straight wire.
[ Bwire ~ (MUnot/4*Pi) (2*I)/r ] *NOTE* MUnot/4*Pi is a constant equal to 1e-7

Since you have Bwire, MUnot/4*Pi, and r (r=0.003) you can now solve for I
[ I = (Bwire*r)/(2*1e-7) ]

(6.116*e-6 *0.003)/(2*1e-7) ]   so I = 0.09174

Now you have to go back to the approximation of the magnetic field of a straight wire.
[ Bwire ~ (MUnot/4*Pi) (2*I)/r ]
BUT now we have a different r value & you now have a I value
your r value is 0.029
Bwire ~ (1e-7) (2* 0.09174)/(0.029) = 6.32*10^-7
The answer for part 1 is 6.32*10^-7

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For part two, you use right hand rule and determine that the direction of the magnetic field at location A, due only to the current in the wire is toward the ceiling.

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