Screen shot of the electric dipole field and detector.

# Electric Multipole Model

The EJS Electric Multipole Model of a point charge (monopole), a dipole, or a quadrupole can show either field vectors or the scalar potential (voltage). A slider changes the charge and a moveable detector shows the electric field direction and magnitude or measures the potential. Detector values can be recorded into a data table and analyzed using a built-in data analysis tool. Users can examine and edit the model if Ejs is installed.

## Exercises:

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. How does the electric field decrease as the detector moves away from the origin (1/r, 1/r2, 1/r3)? Verify that this is true for the simulation. Click on the Potential button to show the scalar potential. How does the potential decrease as a function of position from the point charge (at the origin)?
2. Now, try the dipole simulation. This is a dipole (a positive and negative charge near each other at the origin). In what direction is the dipole oriented? How do you know?
3. 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.
4. How does the field drop off in the y-direction? (Clear the x-axis data and record electric field data for the y-axis.)
5. How does the potential change as a function of position along the y-axis?
6. A quadrupole is constructed from four charges or two dipoles (pointing in opposite directions). How does the field 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?
7. How does this compare with a magnetic dipole? magnetic quadrupole? (See Magnetic Multipole Field model.)

### References:

- Giancoli, Physics for Scientists and Engineers, 4th edition, Chapters 21 and 23 (2008).

### 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/> and in the OSP ComPADRE collection <http://www.compadre.org/OSP/>.