Question 10: A bar magnet is dropped inside a long vertical tube. If the tube is made of metal, the magnet quickly approaches a terminal speed, but if the tube is made of cardboard the magnet falls with constant acceleration. Explain why the magnet falls differently in the metal tube than it does in the cardboard.
Terminal speed in this case may the constant speed the falling magnet attains under the influence of the gravity and the force due to the interaction of the magnetic fields.
See the figure. The bar magnet has a magnetic field. When it approaches the tube, the magnetic flux (i-e, number of magnetic lines of force) linking the tube increases. From our study of the electromagnetic induction, an emf and hence a current, is induced in the tube. According to Lenz’s law, the polarity of the induced current is such that the associated magnetic field opposes the cause of the current (motion of the magnet which increases the magnetic flux on the tube). Therefore, magnet is now moving under the action of two forces. The force of gravity and the retarding force due to the interaction of the two magnetic fields (one due to the falling magnet and the other due to the induced current in the tube). As the bar magnet falls down (under gravity), the flux linking the tube also increases which increases the induced current and the associated electromagnet. A time reaches when the force of gravity is equal to the force of the magnet and the resultant force is zero, as they both are anti-parallel. So in the absence of an unbalanced force, the magnet is falling with constant a constant terminal speed.
Whereas on the other hand, when the tube is made of cardboard, no induced emf (and hence current) is produced. Therefore, the magnet falls freely under the action of the single gravity with constant acceleration g like any other free falling body.