Screen shot of the test charge in a scalar field.

# Electric Potential Trajectory Wrong Model

The EJS Electric Potential Trajectory Wrong model shows a test charge in an external electrostatic potential and the associated electric field. The user can type in an expression for the potential and see the (incorrect) trajectory of the particle. Users can examine and correct the model if Ejs is installed.

## Exercises:

1. Run the simulation. The plot correctly shows the potential and electric field. The initial potential: U(x,y)=-1/(x*x+y*y)^(0.5) is the potential due to a negative point charge at the origin. Show how to get into the form you are more familiar with. You can type new values of the potential as a function of x and y in the input box and you can try new initial conditions and observe the motion.
2. Even though the plot of the potential (and equipotential contours) as well as the electric field vectors are correct, the trajectory of the yellow charged test particle* is incorrect. Push the reset button and then start the model and observe what happens. What should happen? Why?
3. If you need help, click on the energy plot check box which shows a plot of kinetic and potential energy (correctly calculated) for the particle. What is wrong? What is your evidence? You may want to analyze the energy data using Data Tool, the built-in data analysis tool (click on the Wrench button). Some notes on using DataTool:

- DataTool automatically draws lines between nearby points and you may find this confusing so you can click on the checkbox with a line through it to remove the connecting lines.
- You can use Data Tool to create plots of mathematical functions of the current data (adding two columns together, for example). Click on Data Builder to create a new column of data by adding a Data Function and entering a new expression (like KE+PE).
- DataTool can provide a Fit to the data in the first two columns. You may need to drag the columns around in order to fit data of interest.
- If you want DataTool to Fit the data to an equation not in the list, you will need to edit the current equation in Fit Builder by double-clicking on the equation and editing it.

4. Once you think you know what is going on, pick a different expression for the potential (one in which you know what should happen) and observe the trajectory and explain what is wrong. What is wrong with this simulation? What is your evidence?
5. If you have EJS installed, now that you have determined what is wrong with the model, correct it. You will need to go to Model->Evolution to make the changes. Describe how you changed it and how you verified your work. Once corrected, describe what happens for the given initial conditions.

*Recall that a test charge is defined to feel the effects of an external electric field, but not change the field itself (therefore, there are no field vectors around it).

1. Advanced: If the moving charge isn't a "test charge," but instead a real accelerating charge, it should (with the initial conditions), spiral into the center (still not in the way it is calculated in this model). Why? Why was this a problem for the Bohr model of the atom?

### References:

- Giancoli, Physics for Scientists and Engineers, 4th edition, Chapter 23 (2008).

### Credits:

The Electric Potential Trajectory Wrong Model was created by Wolfgang Christian and Anne J. Cox using the Easy Java Simulations (EJS) authoring and modeling tool. Exercises written 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/>.