## Coulomb's Law and Electric Field Package Applet Page

### Coulomb's Law and Electric Field Package: Multipole Field Applet

The EJS Electric Multipole Model of a point charge (monopole), dipole, or a quadrupole showing the electric field. A slider changes the charge and a moveable detector shows the electric field direction and magnitude. A second window with a data table opens as well allowing for recording and analysis of detector values.

Student Worksheet

1. Run the simulation of a monopole (point charge) at the origin. Move the detector around in the electric field and observe the value of the electric field. When the detector is moved twice as far from charge, what happens to the electric field (Record Data if you need to)? Is this consistent with the equation for the electric field of a point charge: E=kq/r2? Explain.
2. Now, try the dipole simulation. A dipole is constructed of two charges: a positive and negative charge near each other centered at the origin. In what direction is the dipole oriented? How do you know?
3. A quadrupole is constructed from four charges or two dipoles (pointing in opposite directions). Can you tell how the charges are arranged? Explain.
4. Optional Data Analysis: How does the electric field decrease as you move away from the origin along the x-axis (1/x, 1/x2, 1/x3, 1/x4)? To find out, move the detector along the x-axis and record the field values in the Data Table. Then try to find a good fit for the data. Note: Clicking on the Wrench button will open up a DataTool with all your recorded data in columns. You may need to move the columns around to Fit the data (the DataTool only fits the data in the first two columns) and you will need to input fit equations in the Fit Builder. For example, if you want to fit the data to a/x2 (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. Under parameters, you will need to click-on and delete parameter "b" and then type your new Function = a/x^2. Be sure you have recorded enough data to be confident that you know how the field drops off as a function of x.
5. Optional Data Analysis: How does the field (in the x-direction) drop off for a quadrupole? To answer this, record an appropriate number of data points (how many do you think are necessary) and fit the data. What do you think happens with an octopole?

There is a second window that opens which contains a data table and allows for use of a built-in data analysis tool.

#### Credits

The Electric Multipole Model was created by Wolfgang Christian, Francisco Esquembre 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/.
Additional information on this applet can be found in the Physics Source comPADRE collection.

#### References

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