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.
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.
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.
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.