Question

In which direction would a compass free to move in the vertical plane point to, if located right on the geomagnetic north or south pole?

Answer 1

At geomagnetic north or south pole, angle of dip is 90°, where horizontal component of earth’s magnetic field B_H is zero. A compass needle can only turn in horizontal plane, so it can point in any direction as B_H = 0, which governs its direction.