Dropping a Magnet Down a Conducting Pipe and Lenz's Law

When a magnet is dropped down a conducting pipe (not magnetic), it falls much slower than expected. This is due to the pipe's ability to conduct a current, which interacts with the magnet's changing magnetic field.

Faraday's law states that a change in magnetic flux induces an electromotive force (EMF) in a conducting loop. As the magnet falls through the pipe, the magnetic flux around it continuously changes, inducing an EMF in the pipe. The magnetic flux is strong near the poles and decreases as the magnet moves away, causing a changing flux both above and below the magnet.

Lenz's law explains the direction of the induced current: it creates a magnetic field that opposes the change in flux. The video uses an analogy of a car slowing down (change in velocity opposite to velocity) or speeding up (change in velocity in the same direction as velocity) to explain how to determine the direction of the change in flux.

At the top of the magnet, the magnetic field points upwards. Since the magnet is slowing down, the change in flux points downwards. According to Lenz's law, the induced current in the pipe above the magnet will create an upward-pointing magnetic field to oppose this downward change in flux. Using the right-hand rule, this means the current flows counterclockwise when viewed from above.

At the bottom of the magnet, the magnetic field also points upwards (towards the top of the pipe). However, the flux is increasing as the magnet approaches. Therefore, the change in flux also points upwards. To oppose this, the induced current below the magnet creates a downward-pointing magnetic field. Using the right-hand rule, this means the current flows clockwise when viewed from above.

The induced magnetic field above the magnet creates an attraction between the north pole of the falling magnet and the induced south pole at the top of the pipe, effectively pulling the magnet upwards. Below the magnet, the induced magnetic field creates a repulsion between the south pole of the falling magnet and the induced south pole at the bottom of the pipe, pushing the magnet upwards. Both effects result in a net upward magnetic force on the falling magnet, reducing its acceleration and making it fall slower.

The magnet experiences a gravitational force pulling it down and an upward magnetic force from the induced currents in the pipe. The net force is still downwards, but smaller than gravity alone, which explains the slower fall. Faraday's law initiates the process, and Lenz's law dictates the direction of the opposing forces.