Free Falling Magnets
By George and Zach
By George and Zach
Click on the video and then the open in a new tab button to watch.
When a magnet falls down a tube made of a material which conducts electricity (we used copper, which is a nonmagnetic metal), its rate of fall tends to be slowed by the magnetic field it creates inside that tube. Lenz's law, created in 1834 by Russian physicist Emil Lenz, explains this relationship, stating that the fall of a magnet down a conductive tube will result in a closed circuit and a subsequent magnetic field that directly opposes the direction of the magnet's fall.
The masses and magnetic strengths of magnets of various shapes and sizes were measured. These magnets were dropped down through a 60 inch long and approximately 0.5 inch wide copper tube (left). As they fell, the time to fall of each from the entry of the tube to the exit was taken.
As you can see (left), the magnets interacted with the copper tube, a nonmagnetic metal, causing them to slow down. We explored the different factors that may have contributed to the speed at which the magnet fell through the tube.
Pictured in this chart are the masses (grams), the average time of fall (seconds), and the magnetism (milliTeslas, measured from a distance of 3 centimeters). The non-magnetic ball exhibits how a non-magnetic material falls much quicker down the tube than the other magnetic ones that we tested. Notice how there is not a direct correlation between the strength of a magnet's magnetic field and the time it took that magnet to fall down the tube.
The five magnets used. Clockwise from top, the stout magnet, the neodymium fragments, the long magnet (misleading name, we know), the rectangular magnet, and the cow magnet.
The fact that all of the magnets took longer than the non-magnetic ball to travel through the tube illustrates that the magnets' interactions with the copper did in fact slow them down.
As you can see, there is no blatant, direct correlation between the strength of the magnetic field a magnet creates and the time it takes that magnet to go down through the tube. The most telling discrepancy in our results is that between the neodymium fragment magnets and the stout magnet. As pictured in the chart above, the two magnets have the same magnetism and approximately the same mass. The only difference between the two magnets was the shape -- the stout magnet had more close contact with the surface of the tube because of its cylindrical shape than the neodymium fragments did. Similarly, the rectangular magnet fell down the tube almost five times as fast as the long magnet even though their magnetic fields are approximately the same and their masses are in the same ballpark.
The instant a magnet is dropped into a tube, an electrical current is induced that flows down the copper tube. This electrical current creates a magnetic field in the opposite direction that interacts with the magnet. The fields cause the magnet to be pulled towards the copper tube and creates resistance. This resistance, however, depends on the shape and mass of the magnet. The neodymium magnet was very thin and had little contact with the copper tube, so it fell relatively quickly. The stout magnet was just shy of being the diameter of the copper tube, so it had plenty of contact that caused significant resistance in its fall. Although the cow magnet had a large surface area that was close to the tube, it was very heavy, so the induced magnetic field was not strong enough to slow it down much. The same can be said for the other longer magnets.
Epsilon = Induced Voltage (EMF)
- = Lenz's Law
N = Number of Turns in Coil
Delta Phi = Change in Magnetic Flux
Delta T = Time
To the left is Faraday's equation for induced voltage which begins with a negative sign in this case due to Lenz's Law. Moving a magnet towards a conducting ring (the copper tube) induces an electric current that flows in a manner such that a magnetic field is created that opposes the field of the magnet, attracting it to the tube and thereby creating resistance even though there is technically only one turn in the coil.
By looking at this equation, it becomes clear that the Magnetic Flux is directly proportional to the Induced Voltage, so theoretically stronger magnets would be affected more. This however, would only be the case if the magnets had the same shape, size, and mass. We learned that these variations played a crucial role in the outcome of our experiment.
Click on the video and then the open in another tab button to watch.
https://www.scienceabc.com/nature/universe/lenzs-law-true.html
https://en.wikipedia.org/wiki/Emil_Lenz