A wire is connected to batteries (not shown), and current flows through the wire

Question

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 4 mm above the needle. The distance d is 6.5 cm. The compass needle deflects 13 degrees from North, as shown. At this location the horizontal component of the Earth's magnetic field is 2e-5 tesla. What is the direction of the magnetic field at location A, midway between the wires, due to the current in the wire? What is the approximate magnitude of the magnetic field at location A, due to the current in the wire? || = T What approximations or assumptions did you make in solving this problem? Assume that at the location of the compass the effect of the distant wire is negligible Assume the bent end of the wire is far from location A Assume one side of the wire is much longer than d Assume the Earth's magnetic field is negligible

Explanation / Answer

Bwire = tan(11)*2e-5 = 3.888e-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) ] so I = 0.058314

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 0.026
Bwire ~ (1e-7) (2*0.058314)/(0.026) = 4.486e-7

The answer for part 1 is 4.486e-7

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