Final answer:
The apparent polar wander paths for North America and Europe vary because they moved independently due to the theory of plate tectonics and cooled below their Curie point at different times. The correct answer is option d.
Step-by-step explanation:
The apparent polar wander path for North America and Europe do not coincide because the continents have moved independently over geological time due to the theory of plate tectonics. The paths differ because the rocks in these regions cooled below their Curie points at different times, which locked in the magnetic signatures at different periods of the Earth's magnetic field history. Geoscientists refer to an Euler pole to describe the motion of the tectonic plates that move in different speeds and directions, which contributes to the differing apparent polar wander paths of North America and Europe.
It is important to note that continental drift, first proposed by Alfred Wegener, further explains why these paths are different due to the previous connections and separations of the continents over millions of years. So, the answer to the student's question is that the apparent polar wander paths for North America and Europe do not coincide because the rocks cooled below their Curie point at different times (option c).