Gaussian surface around a long line of charge.

# Linear Charge Gauss's Law Model

The EJS Linear Charge Gauss Law model shows a Gaussian surface and allows for the measurement of the charge enclosed and surface area of the surface. Users can change the radius of the linear charge as well as the size of the Gaussian surface. Users can examine and edit the model if Ejs is installed.

## Exercises:

1. Run the simulation. The long blue cylinder is a very long line of charge. Change the height of the Gaussian surface by dragging the red handle. How does the charge enclosed and surface area change as you change the height of the Gaussian surface? Record some data for different heights. Why doesn't the ratio of qenclosed/area change?
2. Now, use the brown handle to change the radius of the surface. Again, how does the charge enclosed and surface area change as you change the radius? If the surface remains outside the long cylinder? Explain. If the surface is within the blue cylinder? Explain.
3. Clear the data (button with Eraser icon) and record data for charge enclosed and surface area for different radii of the Gaussian surface (moving the handle). Collect enough data so you can plot how the ratio of qenclosed/area as a function of the radius, r, of the Gaussian surface. Determine electric field as a function of r both inside and outside the blue cylinder. You can use the built-in Data Tool by clicking 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.
- DataTool can provide a Fit to the data in the first two columns only. 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. For example, if you want to fit the data to a/x3 (and have the program automatically find the value of a), double-clicking on the equation of the line (a*x+b) will automatically open the Fit Builder. In this case, since you only want to fit one parameter, first delete parameter "b" (from the parameter list) and then type your new Function = a/x^3.

4. For uniformly charged wire (charges evenly distributed throughout) of radius R, the electric field as a function of radius is given by

E ∝ r for r<R (inside wire)
E ∝ 1/r for r>R (outside wire)
but this simulation does not give this result. What is different?

5. Advanced: This model does not model a uniformly charged wire, instead the charge is distributed unevenly (along the radius) in the wire. What is the charge distribution?
6. If you have EJS installed, change the model so that it models a charge distributed evenly in the wire. You will need to go to Model->Fixed Relations. Describe how you changed it and record the data from your edited model.

### References:

- Giancoli, Physics for Scientists and Engineers, 4th edition, Chapter 21 (2008).

### Credits:

The Coulomb Force Wrong Model was created by Anne Cox, Wolfgang Christian,and Francisco Esquembre 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/>.