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Assumptions:

  1. An iron particle is negligibly light and small.
  2. Only the path during acceleration is important. It is less important what happens once it is already inside the solenoid (while still interesting, if you know what happens after that).

Question: - Will it fly along the magnetic flux lines?

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Not exactly. The force exerted on an iron particle in a magnetic field is in the direction in which the field gets stronger. There is no net force if the field is uniform. However, imagine what happens if the particle has a velocity when it is far from the solenoid. The magnet will deflect the particle, but the particle's path will obviously depend on its initial position and velocity; so the particle's path will not in general follow the flux lines.

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