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:
- 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)?
- 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?
- 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.
- How does the field drop off
in the y-direction? (Clear the x-axis data and record electric field
data for the y-axis.)
- How does the potential
change as a function of position along the y-axis?
- 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?
- 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/>.
