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 = 6.11e-6

We need to use approximation of the magnetic field of a straight wire.
[ Bwire = (MU0/4*Pi) (2*I)/r ]

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 = 6.11e-6*0.003/2*1e-7 = 0.09 A

Now you have to go back to the approximation of the magnetic field of a straight wire.

BUT now we have a different r value & you now have a I value
your r value is 0.029

Bwire = (1e-7) (2*0.09)/(0.029) = 0.63e-7 T

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