# A bar magnet falls through a long hollow metal cylinder fixed with its axis vertical. What is the...

## Question:

A bar magnet falls through a long hollow metal cylinder fixed with its axis vertical.

What is the final acceleration of the magnet ?

When the magnetic flux through a material circuit changes it will induce an EMF. The EMF drives a current. This current will in turn set up a magnetic field. This induced magnetic field opposes the change in the applied field. According to Faraday's law, the induced EMF is proportional to the rate of change of the magnetic flux. This is simply a manifestation of Le Chatelier's principle.

When a bar magnet is dropped into a metal tube with its dipole moment along the axis of the tube then as it falls and approaches the tube the magnetic flux through the tube will start increasing. The induced EMF within the metallic body of the tube will drive circumferential currents along the surface of the tube. These currents set up their own magnetic moments. The polarity of the induced moment is in such a way that it opposes the incoming magnet. As the speed of the incoming magnet increases due to gravitational acceleration so does the induced EMF proportionately. Therefore the opposing magnetic moments will also increase in magnitude. The magnetic repulsion will finally become equal to the gravitational attraction. Thereafter the acceleration of the magnet becomes zero. The magnet attains terminal velocity. It will now glide down along the axis of the tube with zero acceleration.