Magnetic Braking of a Falling Magnet
A strong bar magnet is dropped through a vertical copper tube of length 1.2 m. A student observes that the magnet falls noticeably slower than a magnet dropped through a cardboard tube of the same length, and that the copper tube becomes slightly warm. The student claims this proves copper is magnetic and attracts the magnet upward, and proposes that a thicker copper tube would make the magnet rise. The magnet's north pole faces downward as it falls. Copper is non-magnetic in the sense of not being ferromagnetic.
1. Explain the observed slowing and warming using electromagnetic induction, and evaluate the 'copper is magnetic and attracts' claim.
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As the magnet falls, the magnetic flux through each horizontal cross-section of the copper tube changes. By Faraday's law, this induces an EMF and hence eddy currents in the copper. By Lenz's law, the induced currents create a magnetic field that opposes the change in flux - so the field from the induced currents pushes upward on the approaching magnet, slowing it. The eddy currents dissipate energy as heat (I²R), warming the tube.
The 'copper is magnetic and attracts' claim is wrong. Copper is not ferromagnetic; there is no static attraction. The force arises only because the magnet is moving and flux is changing. A stationary magnet in the tube would experience no upward force. The slowing is a dynamic, induction effect, not magnetic attraction.
2. Evaluate the proposal that a thicker copper tube would make the magnet rise, and state what a thicker tube would actually change.
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The proposal is wrong. The upward force from eddy currents can at most oppose the magnet's motion; it cannot exceed the weight and reverse the motion, because the induced currents depend on the magnet's motion - if the magnet stopped, the flux would stop changing and the force would vanish. There is no mechanism for sustained lift.
A thicker tube has lower electrical resistance for the eddy current paths, so for the same induced EMF the currents are larger and the opposing force is stronger (and heating greater). The magnet would fall more slowly, not rise. The terminal behaviour is a slower descent, set by the balance between gravity and the velocity-dependent magnetic drag.