A Demonstration of Lenz's Law

What

Lenz's law is fascinating. As we grow up and we experience the world we build a mental model of our surroundings and fortify our understanding of how things ought to work. We know that if you throw a ball up in the air it will arc upwards before speeding up towards the ground, if you put water in a freezer, it'll slowly get colder until it changes phase into ice, but if you drop a magnet through a copper tube... it doesn't do what you' expect. It's a nice demonstration of eddy current, electricity, and magnetism that we don't typically get a chance to see in everyday life. I think science is cool like that, it forces you to break your mental model and develop new models to account for our ever changing landscape. Lenz's law is a special version of this since it's easy to reproduce and show to others.

Lenz's law describes a phenomenon where an electric current which is induced by a changing magnetic field (commonly a moving magnet) will create a force impeding motion. This force is commonly applied as a braking force for trains, roller coasters, and electric cars where some of the generated current is used to charge the car's battery. Lenz's law is also used in some electric generators and inductors.

A wooden board with three tubes made from acrylic, aluminum, and copper attached.

Why

When I was a part of the Caltech Mentorship program every mentee had to design an experiment, gather data, and present it at the end of the year to a panel of industry professionals to show what we had learned during the program. I always felt that visuals are one of the most important parts of presentation and wanted to have a physical demonstration instead of just some video and data. To me, Lenz's law is one of the coolest visual science demonstrations out there and had the potential for me to incorporate some basic computer vision and data collection.

Position versus time of a magnet falling through an acrylic, aluminum, and copper tube.

How

To show Lenz's law, I designed a basic demonstration consisting of three pipes, each made of a different material, aluminum, copper, and acrylic. This would allow me to show how Lenz's law changed depending on the materials involved, it would also allow me to gather the necessary data to calculate the strength of my magnet. To track the magnet as it fell, oblong holes were drilled into each of the metal pipes, this let me gather the position and time when the magnet entered and left each viewing hole using some basic Python with OpenCV.

By plotting this data I found the acceleration of the magnet throughout the fall. Since the acceleration of gravity and the weight of the magnet were known, I could find the magnetic force that was exerted. This could then be used to find the magnetic dipole moment which was calculated as 3.21E-8 for the copper pipe and 2.55E-8 for the aluminum pipe. The presentation was made using LaTeX.