2 magnetic fields

This isn't really a home work question but i think it belong in this section, since we are starting to play with compasses in class
1. The problem statement, all variables and given/known data
I was thinking what direction would a compass point if it was placed near a magnetic field (say from a loop of wire) which is at right angles to Earths magnetic field, so then you had two magnetic fields (Earth's and the loop) which will affect the compass


2. Relevant equations
Amperes Law and/or Biot-Savart Law


3. The attempt at a solution
I can see how the compass would point in between the north of the two magnetic fields but at what degree?
here's my attempt at, is it right? so visualise a line from an origin to a point on the xy plane with the strength of the loop is the x distance and the strength of Earths field is the y distance, so the line will end at x,y or B(loop), B(Earth) and now take the line and the y=0 line and you have your angle change.
I have two questions from this,
Firstly am i right in saying the magnetic field will change directions if it is above the loop or in the loop (the right hand rule)? there has got to be a relation ship depending on the distance away from the loop, what is it?
And secondly will the magnetic field strength of the loop drop (spread out) if it is over a larger loop (as in will the magnetic field of the other parts of the large loop affect the compass), how do I calculate for this? or will this be insignificant change to the compass?

any help on any part would be great
 

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