# There is a bar magnet falling through a metal ring. The first metal ring is solid all the way...

## Question:

There is a bar magnet falling through a metal ring. The first metal ring is solid all the way around but in the second metal ring, it has been cut through. Why is the motion in the magnet with the solid metal ring retarded when the magnet is above the ring and below the ring? What induced currents appear in the ring? Why is motion unaffected in the ring in part 2?

## Le Chattelier's Principle In Electromagnetism

Le Chattelier's principle governs the general behavior of equilibrium systems in nature. If a system in equilibrium is disturbed then it will respond by trying to annul the disturbing cause. In the context of varying magnetic fields, the principle manifests as Faraday's law. If the magnetic flux through a material loop changes then the loop will respond with an induced EMF and an associated current. The magnetic moment due to the current will have its poles aligned in such a way that the induced magnetic flux tries to cancel out the causative flux change.

## Answer and Explanation:

When a bar magnet is dropped through a metal ring the magnetic flux through the ring will start increasing initially. As a result circulating currents are induced on the surface of the ring. Now, corresponding to a circular loop of current there is a magnetic moment with its magnitude equalling the product of the current and the area. The associated magnetic moment will repel the incoming bar magnet. As gravity accelerates the incoming magnet the induced opposition will increase. At some point, the magnet crosses the ring. Now as it recedes the flux through the ring will start decreasing. Therefore the ring will respond by using its induced magnetic moment to attract and prevent the bar magnet from falling. Thus the bar magnet is slowed down when it approaches the ring due to repulsion and after it crosses the ring due to attraction.

If instead of the ring it is a hollow metallic cylinder then at some stage the repulsion due to the induced magnetic moment will equal the attraction due to gravity. So now the bar magnet will attain terminal velocity and glide down gently. In fact, the terminal velocity is attained quite quickly.

If the metal ring has a cut, the EMF is not able to drive the current through a closed-loop since the circuit is open. Hence there is no associated induced magnetic moment. Consequently, the falling magnet does not experience any opposition and will undergo free fall.