Magnet falling through three conducting loops and induced magnetic field.

# Falling Magnet Eddy Current

The EJS Falling Magnet Eddy Current Model shows a magnet falling through conducing loops. The model shows the induced field and induced currents (Eddy currents). It plots the velocity of the falling magnet as a function of time. The number of conducting loops, resistance and spacing between the loops are all adjustable parameters. Users can examine and change the model if they have Ejs installed.

## Exercises:

1. Run the simulation. A magnet falls through several conducting loops under the influence of gravity:

- A falling magnet induces current. Why? The yellow or green arrows that go around the loops show the direction of induced current and the width of each is proportional to the current.
- This current, in turn, induces a magnetic field. Why? Note that the induced field is shown, but not for every time step of the simulation as it would slow things down too much to compute the field for every time step.
- Finally, the induced field provides a force on the falling magnet. Why?

2. Click on the Magnet check-box (at the top of the window). When this box is unchecked, it simulates a non-magnet of the same size and mass falling through the loops. How can you tell this is not a magnet?
3. From the direction of the current arrows shown (yellow/green), can you determine the orientation of the falling magnet (north pole on the bottom or south pole)? Why or why not and if so, what is the orientation?
4. What happens if you change the number of loops, the spacing and the resistance (of each loop). Explain your observations.
5. Try adjusting things so that the magnet reaches an almost constant velocity for a short period. What did you need to do for this to happen? At this point, the magnet reaches terminal velocity within the conducting loops. A common demonstration is to show a strong magnet dropped through a copper (or other non-magnetic material) tube. Using this simulation, explain your observation.
6. Note that this simulation neglects the changing flux through one loop due to the changing magnetic field in nearby loops (i.e. the induced current is only in response to the falling magnet) as well as the loops' self-inductance.

### References:

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

### Credits:

The Falling Magnet Eddy Current 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/>.