Final answer:
A magnetic compass needle aligns with local magnetic field lines, which can be visualized using the right hand rule around current-carrying wires. The field lines form circular loops, with the needle orientation changing when flying across different longitudes due to Earth's non-uniform magnetic field.
Step-by-step explanation:
In the scenario of a compass being used near a current-carrying wire, magnetic field lines form that are concentric circles centered on the wire. According to the right hand rule, if you point your right thumb in the direction of the current, your fingers will curl in the direction of the magnetic field, as seen in Figure 22.37(b). This principle helps us map out the magnetic field around the wire. Furthermore, a compass needle aligns itself with the local magnetic field, with its north pole pointing towards the south magnetic pole of the Earth, which is near the geographic North Pole.
When flying due west along the equator, the orientation of the compass needle will change as your longitude changes because the Earth's magnetic field is not uniform. As you pass the prime meridian, the compass needle is perpendicular to your motion, but as you keep flying, the angle will change due to the variation in the Earth's magnetic field with respect to your new position.