Modeling the Magnetron Toy

• Main Author: Chris Dubois
• Other Authors: The Pennsylvania State University CiteSeerX Archives
• Format: Text
• Language: English
• Published: 2005
• Subjects: North Pole
• Online Access: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.511.8536; http://www.ics.uci.edu/~duboisc/archive/MagModel.pdf

Many real-world phenomena are often too complex for us to capture entirely using mathematical tools, but a careful approach enables an exploration of that complexity and may provide insight into the phenomena. The author found a simple desk toy, the “Magnetron, ” to be a perfect target for exploration: while simply designed and constructed, one quickly realizes the system has very complex dynamics. The toy features two rotors, spaced slightly apart, with magnets mounted at the end of each arm; manually spinning one rotor causes the other rotor to spin due to the interactions between the magnetic fields. In this paper we present a mathematical model that successfully reproduces several of the toy’s behaviors. In the future we hope to explore the transitions between various equilibria of the system. The Magnetron The Magnetron toy has two plastic rotors mounted on a wooden block by metal spindles that serve as axles. Each rotor has three evenly spaced arms. At the end of each arm, there is a small bar magnet mounted inside a plastic housing with its North pole oriented away from the rotor center. The two rotors are spaced such that they nearly touch when they are closest to each other. Since dipoles are subject to forces due to external magnetic fields, the fields produced by the magnets in one rotor affect the rotation of the opposite rotor and vice versa.