Screen shot of co-centric spheres (a) electric field and (b) equipotential.

# Electric Field and Potential Model

The EJS Electric Field and Potential Model shows the electric field and potential for cylindrical and spherical symmetry. In both symmetries, there are co-centric charged surfaces where the outer surface is grounded. The model reports the force on a test charge (yellow) between the co-centric surfaces as well as the voltage. Information about EJS is available at: <http://www.um.es/fem/Ejs/>.

## Exercises:

1. Books often show two-dimensional representations of electric field vectors. Notice, for example, that the two-dimensional representation of co-centric cylinders and co-centric spheres are the same:

   Suppose you have a flat sheet of material with charged conductors. Would you expect the electric field and potential to be more like that of (a) sphere or (b) cylinder? Explain.

2. Run the simulation. You can zoom in (Shift-Click-Drag), rotate (Click-Drag) or pan (Ctrl-Click-Drag) the 3D views. What are the differences do you observe in the functional form of the electric field vectors between the cylinder and sphere?
3. How does the Equipotential Plot change for the spherical or cylindrical symmetry as you change z-location (moving the z-slider) of the plane? Explain.
4. If z=0, how can you differentiate between the contour plots for each geometry? In lab, you are going to measure the potential at a variety of points on a two-dimensional surface and compare it to calculated values to determine if it mimics the cylinder or sphere. Open Laboratory Instructions.

### References:

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

### Credits:

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