How many magnetic poles?

Last weekend I presented at the Exploratorium's 4th Annual NGSS STEM Conference "Making Science Count: Integrating Math into an NGSS Classroom." I presented a few inverse and inverse square relationships participants explored using hands on experiments. One of them was to investigate the relationship between the strength of a magnetic field and the distance to the object.

Thanks to sponsors, participants were able to go home with their own "cow magnet" (if you don't know why they are called that read about Hardware Disease). While preparing for the workshop that morning senior scientist and staff physicist Paul Doherty cautioned me that while I would expect cow magnets to be dipoles they could be tripoles. After he check with magnetic viewing film it turned out they were quadpoles. And that can complicate an experiment.

Workshop participants either borrowed my Vernier Magnetic Field Sensor or used the magnetometer on the Physics Toolbox app during the workshop. When I was preparing for the workshop I found that this could be an inverse square or an inverse cubed relationship depending on the physical dimensions of the magnet. Given the orientation of these quadpole magnets if you rotated the cow magnet at all as it approached the sensor the polarity could change.
1. Asking questions (for science) and defining problems (for engineering)
Below is a video using a dipole donut magnet, a dipole cow magnet and a quadpole cow magnet that models what I would expect students to see.

I investigated further using my Vernier Magnetic Field Sensor once I got back to school. Below is a graph made by starting the sensor perpendicular to one end of the cow magnet and then moving up the length of the cow magnet to the other end. I put a pencil in between the cow magnet and the sensor to maintain the same distance between them.

On the left, the red line was made using a dipole cow magnet and the blue by the quadpole magnet. In this case they are similar and one might conclude that they are both dipoles. (Differences in slope are due to the sensor's speed.) On the right, the red line is the same, made with the dipole magnet. The orange and green were both made with the quadpole magnet. When the green line was made the magnet must not have had a pole directly facing the magnetic field sensor.

I also pointed the sensor at the end of the cow magnet and rolled it along the table, keeping the sensor from rolling and at the same distance away. I tried it twice with the quadpole magnet, creating the green and purple lines in the middle. This was harder to keep steady but you can see the polarity switch as the lines pass the time axis. Repeating the experiment with the dipole created the brown line at the top of the graph. For the dipole rolling it made no difference in the polarity strength or direction. 

So what can you do with a pesky quadpole cow magnet? Why, confuse your students of course! I plan to hand groups of students one dipole and one quadpole cow magnet and ask them to determine the number of poles on each. If they are lucky they will get a compass and/ or viewing film. Otherwise having two magnets should be interesting enough. If you're keeping track of the NGSS Science & Engineering Practices, such an investigation could lead to quite a few of them in one lesson:

2. Developing and using models [of thinking]
3. Planning and carrying out investigations
4. Analyzing and interpreting data
5. Using mathematics and computational thinking
6. Constructing explanations (for science) and designing solutions (for engineering)
7. Engaging in argument from evidence
8. Obtaining, evaluating, and communicating information