Magnet falling above a superconducting loop and the induced magnetic field.

# Falling Magnet Superconductor

The EJS Falling Magnet Superconductor Model shows a magnet falling toward a superconducting loop. The model shows the induced field and induced currents (Eddy currents). It plots the position and velocity of the magnet as a function of time. The size of the superconducting loop (and thus its inductance) can be changed. Users can examine and change the model if they have Ejs installed.

## Exercises:

1. Run the simulation. A magnet falls toward a superconducting loop under the influence of gravity with an arrow that shows the magnetic force on the falling magnet:

- A falling magnet causes a changing flux in the loop. Why?
- The loop produces a back emf (and associated current related by emf=L(di/dt)) to balance the externally induced emf. Why?
- Finally, the induced current produces a magnetic field that provides a force on the falling magnet. Why?

2. Why doesn't the magnet pass through the loop?
3. The magnet oscillates above the loop. Is the motion simple harmonic? Explain. You can damp the motion using the v=0 bottom so the magnet will be suspended above the loop.
4. When you change the size of the loop, how does the self-inductance of the loop change? Why? How does the motion change for different values of the radius? Note that not only does the inductance change, but the induced magnetic field is different because of a different induced current but also because of the different loop size (the field on axis of a loop goes approximately as the inverse of the radius).

### References:

- PIRA 200: Superconductors. 5K20.25 (includes related references).
- Giancoli, Physics for Scientists and Engineers, 4th edition, Chapter 29 (2008).

### Credits:

The Falling Magnet Superconducting Model was created by Anne J Cox using the Easy Java Simulations (EJS) authoring and modeling tool .

You can examine and modify a compiled EJS model if you run the program by double clicking on the model's jar file. Right-click within the running program and select "Open EJS Model" from the pop-up menu to copy the model's XML description into EJS. You must, of course, have EJS installed on your computer.

Information about EJS is available at: <http://www.um.es/fem/Ejs/> and in the OSP ComPADRE collection <http://www.compadre.org/OSP/>.