# Falling Loop Model

The EJS Falling Loop Model shows a conducting loop falling out of a region of uniform magnetic field. It also plots the velocity of the loop as a function of time. Users can change the size the the loop, the orientation of the loop to the field, the size of the field and the location of the loop and field. Ejs must be installed to complete this activity.

## Computational Modeling:

1. Run the simulation. The arrows show the uniform magnetic field. A conducting loop falls under the influence of gravity, but it also experiences a force as it leaves the region of magnetic field. What is causing this upward force? (Hint: There is an induced current in the loop. Why? This means there is a magnetic force in what direction(s) on the side(s) of the loop?) How can you tell from looking at the plot that the force on the loop is non-constant for part of the fall? Once the loop is completely out of the field, the force is constant. Why? What is the acceleration?
2. Run the simulation again, but this time set the angle to ± 90o. Explain what you observe. Why does the angle matter?
3. Currently, there is a magnetic field in the x-direction called Bx (Navigate to Model->Variables->Constants(Tab) to see where it is defined). Add an input field or slider to the so you can change Bx from 0 to 1 (Navigate to the View and in the Interface palette, find a panel and add it in the topPanel in the main drawingFrame (clicking on the panel turns your cursor into the "Magic Wand" which allows you to add it to the View). Find the appropriate Interface to put in your new panel and change its properties so that it controls the variable Bx.
4. Advanced: Add to the View a way to control By as well. Even though the field vectors show a change in By (variable is defined in Model->Variables->Constants(Tab)) you should verify that it is not yet included in the model for the magnetic force that acts on the loop (when it is moving from the region of uniform field). To add it to the model, you will need to modify the calculation of the acceleration.

- Navigate to Evolution and click on Prelim Code button to see the equation for the acceleration. The first line of the code finds the x-component of the magnetic field on the top wire by calling the getBx() method.
- Navigate to Model->Custom->getField(Tab) to notice that there is a similar method for getting the y-component. Navigate back to the Prelim Code and include the necessary lines to get the value of the y-component of the field and change the calculation of the flux and the force to appropriately to include By. Document your changes.
- Verify that your model is correct by setting Bx = 0, By = 1 and checking that the loop does the correct things when it is parallel and perpendicular to the field vector. Check it at another value of Bx and By (both non-zero) and explain how you verified that your model is correct.

### References:

- Giancoli, Physics for Scientists and Engineers, 4th edition, Chapter 29 (2008).

### Credits:

The Falling Loop Model was created by Wolfgang Christian and Anne J Cox using the Easy Java Simulations (EJS) authoring and modeling tool. The exercises are by Anne J Cox.

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/>.