**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