Screen shot of the magnetic dipole field and compass.

# Magnetic Multipole Field Model

The EJS Magnetic Multipole Field Model shows the field of a magnetic dipole or quadrupole with little compasses that indicate direction and relative field strength. A slider changes the angular orientation of the dipole and a movable compass shows the magnetic field direction and magnitude. Compass 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 dipole. Move the compass around in the magnetic field of the dipole (sitting on the origin) and observe the value of the magnetic field. What direction is the dipole oriented on this simulation (x-axis or y-axis)? How can you tell? If this dipole were generated by a current carrying loop, how would it be oriented on the simulation (draw a diagram)? Change the angular orientation of the dipole (or current carrying loop) and describe what happens.
2. The magnetic field decreases as you move away from the dipole (origin). Along the x-axis does it decrease as 1/x, 1/x2, 1/x3, 1/x4? In order to find out, move the compass along the x-axis and record the field values in the Data Table. (do not make measurements too close to the dipole which is at the origin). 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 (drag the columns in the DataTool) to Fit the data (the DataTool only fits the data in the first two columns). You will need to input different 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-click in the Fit Equation box. Edit the fit equation from a*x+b to a/x^2 and since you are only fiting one parameter (named "a"), under Parameters, highlight "b" and cut it and then type your new Function under = 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.
3. How does the field drop off in the y-direction? (Clear the x-axis data and record magnetic field data for the y-axis.)
4. A quadrupole is constructed from 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.
5. Adding more dipoles does not necessarily change the way the field decreases as a function of position. Choose one of the configurations of multiple dipoles. The yellow arrows show the position and orientation of the dipoles. How does the field along the x-axis decrease as a function of position for one of these? (Again, do not try to measure the field right on top of one of the dipoles.) Is it closer to a dipole or quadrupole field?
6. How does the magnetic dipole compare with the electric dipole? magnetic quadrupole compare with electric quadrupole? (Check Electric Multipole Model for comparison.)

### References:

- Giancoli, Physics for Scientists and Engineers, 4th edition, Chapter 27 (2008).

### Credits:

The Magnet Multipole Field Model was created by Wolfgang Christian and Francisco Esquembre and modified by 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/>.