To Create a Triple Well Potential with a Speaker Magnet
If a potential has a minimum it gives the stable equilibrium position and the system can oscillate about it. Potentials with more than one minima are much more interesting as it allows hopping between different stable positions and so on.
A speaker magnet gives rise to a cylindrically symmetric magnetic field. What kind of potential will it provide to small ferromagnetic object, which is allowed to move on the circular boundary on its curved surface? Obviously it will be a constant potential and the object can be stuck to any point on this surface. But real interesting potential results if you fix one such object on the magnet and look for the potential on a similar other object.
A speaker magnet, two ball bearing ball
- Stick a ball bearing ball on the inner curved surface of the magnet. Do it at several places and see that it sticks at any point on this surface. This is because of the cylindrical symmetry of the magnet.
- Let the ball stick at one position and take another similar ball bearing ball. Try to stick it at different positions on the inner curved surface. At how many positions does the ball stick? There are 3 such position.
- At each such position, shift the ball a little and release. What do you see of the ball?
- Can you qualitatively find, at which of the 3 positions, is the restoring force (or the force constant) largest. For this position the frequency of oscillation about the equilibrium position should be largest.
- From your observation, qualitatively draw a plot of potential vs angular position of the second magnet taking the first magnet to be at \(\theta=0\).
- Remove both the balls. Repeat steps 1-3 with balls placed on the outer curved surface. Write your observations.
Figure to be made