Compass deflection by overhead transmission lines

[SQUIDDO]

Problem Description:
A hiker is reading a compass under an overhead transmission line that is 5.1m above the ground and carries a current of 807A in a horizontal direction from North to South. Assume the Earth's field is of the order 0.5*10^-4T.

A) Determine the magnitude of the field produced by the transmission line at a point directly underneath

B) Due to the transmission line, the compass will be deflected by a certain angle instead of pointing north. Find this angle in degreesRelevant equations:
1. Magnetic field of a straight conductor at distance 'd' = (μ/4π)*(2I/d)
Attempt at Solution:
Using the equation above and a given value for mu, I was able to find the strength of the magnetic field directly underneath the wire as being 3.164*10^-5

As for the next step, I'm totally lost. I was thinking of finding the forces on the compass due to the transmission line compared to Earth's field, and using vector lines to find the deflection, but I have no idea of the charge on the compass or anything.

I also thought I could just take the relative directions and sizes of the Earth's field and then draw vectors from there, but I don't know if that's allowed.

What can I do? Thanks for your time!

 

[TSny]

I also thought I could just take the relative directions and sizes of the Earth's field and then draw vectors from there, but I don't know if that's allowed.

Yes, it's allowed . What do you get? (You don't need the "charge" of the compass. Just figure out the direction of the net magnetic field.)

 

[SQUIDDO]

In that case, I draw two vectors to represent the magnetic field directly under the wire due to the wire (A), and due to the Earth (B).

Assembling them head-to-tail, tan(theta) = B/A
So theta must be ~33 degrees, which is right! Thanks!