Falling Magnet Applet

This applet presents the fields of a permanent magnet of magnetic dipole moment M falling though a non-magnetic copper ring with resistance R and self-inductance L. To start the animation hit the "Go" button. The applet caculates the motion of the magnet by solving three coupled ordinary differential equations using a 4th order Runge-Kutta scheme (from Christopher Oie, Inc. see below for acknowlegment) and then plots the field lines as the magnet falls, in real time. The meter in the animation shows the magnitude and direction of the eddy current in the ring. You can change the resistance of the ring and the magnetic dipole moment by using the scroll bars at the bottom of the screen. You can change the time of the animation by using the "T" scroll bar at the bottom of the screen. After changing these hit "Restart" and then "Go" again. A poster presented at the January 1999 AAPT Meeting (PDF file) explains some of the mathematics and physics of this animation. See pages 5, 6, and 7 of this document, especially equation 14 on page 7, for the differential equations we are solving to get the motion of the falling magnet. The parameter called "Resistance" ("Dipole moment") below is the paramter "alpha" ( the square root of the parameter "beta") in equation (11) of this paper.

If you would like to see a slower version of this applet which shows the electric and magnetic vector fields of this system as the magnet falls, follow this link.
Note: previous to November 6, 1999, there was a minor error in this applet which has now been fixed, and also a change has been made in the definition of one of the input parameters.

The core of our 4th order Runge-Kutta applet code is Copyright (c) 1997 by Christopher K. Oei, Incorporated. http://www.chrisoei.com; info@chrisoei.com Permission to use, display, and modify this code was granted by Christopher Oei, Inc. provided that: 1) this notice is included in its entirety; 2) Christopher Oei, Inc. is notified of the usage.