Distance of compass to wire based on magnetic field strength

[songoku]

Homework Statement

As shown in Figure 1 below, a long, straight conducting wire is stretched horizontally directly above a magnetic compass, both of which are separated by distance d. When electrical current is not flowing through the wire, the compass needle points in a direction parallel with the wire’s direction. When a current flows through the wire, the north pole of the needle rotates 60^o to the east and comes to rest. Next, as shown in Figure 2, while the current continues to flow, the wire is moved vertically upward to a position distance from the compass. As a result, the north pole of the needle rotates and comes to rest position pointing 45^o east of north. What is the value of D/d ?

Homework Equations

Maybe:

B = (μ_o I) / (2πd)

The Attempt at a Solution

The compass in figure 1 has bigger angle because the magnetic field is stronger but I don't know what formula relates the value of magnetic field produced by a very long straight wire to the angle of deflection of compass.

 

[gneill]

Why do you suppose the compass was pointing in the direction it was when there was no current in the wire (what does a compass "measure")?

 

[songoku]

Why do you suppose the compass was pointing in the direction it was when there was no current in the wire (what does a compass "measure")?

Ah I get it. Thanks a lot for the hint

 

[gneill]

You're very welcome