Screen shot of the test charge in the 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 point charge at the origin. Explain 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. 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 play it and observe what happens with the initial conditions. What should happen? Why?
2. If you need help, click on the Hint 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.):
4. Once you think you know what is going on, pick a different value for the potential (one in which you know what should happen) and observe the trajectory and explain what is wrong.
5. What is wrong with this simulation? What is your evidence?
6. 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.

*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).

### 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/>.