Magnetic Fields Produced by Currents

[bobbworm42]

A long, straight wire is oriented in the north-south direction, and the current in the wire is directed to the north. The horizontal component of the Earth's magnetic field is 4.5 x 10-5T and points due north. A small horizontal compass needle is located directly below the wire, 1.9 cm from it. The compass needle points 40° north of west. What is the current in the wire?

So I know that:

B(horz.) = 4.5 x 10-5 T
r = .019 m
Theta = 40° North of West

I have tried combing F = ILB sin theta and B= (U(0) I)/(2*p* r), but I can find no place to incorporate my theta or how to find the vertical component of the Earth's magnetic field (if it is even needed).

Please show me the error of my ways.

 

[Mindscrape]

You may be over complicating the problem. At the bottom of the wire the magnetic field is pointing in the west direction with some magnitude based on how far away it is and how much current flows (you only know one of these). The Earth's field is pointing in the north direction. It's a vector problem.