Levitating Magnet Applet

Instructions

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 meter in the lower right shows the magnitude and direction of the eddy current in the ring. A positive meter reading (to the right) means that current in the ring is moving counterclockwise as viewed from above the ring. We also indicate the direction of current in the ring on the ring itself, in red.

You can change the resistance of the ring R and the magnetic dipole moment of the falling magnet M 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.

If you want to see what the vector magnetic field representation (that is, showing the direction of the magnetic field on a grid across the canvas, with the color of the (constant) vector coded to indicate the strength of the magnetic field (bluer for stronger field, whiter for weaker field), hit the "Toggle B Field" button (but be forewarned, this really slows things down!). To get rid of this hit the "Toggle B Field" button again. You can do the same with the electric field and the "Toggle E Field" button, although here since the E field is always either into or out of the page, we just indicate that, again with color coding to indicate field strength (greener for stronger E field). Again, you must always hit "Restart" before hitting "Go" after you have made any changes of this kind.

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. 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" above corresponds to the parameter "alpha" in equation (11) of this paper. The parameter called "Dipole Moment" above corresponds to the square root of the parameter called "beta" in equation (11) of this paper.

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.

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 as of that date ("Dipole Moment").