Hello, I\'m sorry for my frustration, but, after working through the six other [

Question

Hello, I'm sorry for my frustration, but, after working through the six other [incorrect] posted solutions for this same problem, I need some help!

Please, might I ask that the posted solution be explicit and easy-to-follow? I'm unsure of what the radius 'r' is supposed to be.

Thank you, in advance, for your time and consideration!

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 5.5 cm. The compass needle deflects 10 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? |B| = ?T

Explanation / Answer

Using right hand rule the direction of the magnetic field at location A, due only to the current in the wire is toward the ceiling.

from right angle triangle

Bwire = tan(10)*2*10^-5 = 3.53*10^-6 T

magnetic filed due to long striaght wire

Bwire = uo*i/2pi*r

r = 5.5 cm

3.53*10^-6 = (2*10^-7*i)/(0.006)

i =0.1059 A

for r = 5.5 cm

B = (2*10^-7*0.1059)/(0.055)

B = 3.85*10^-7 T

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