Screen shot of the test
charge in the field.
Electric Potential Trajectory
Wrong Model
The EJS Electric Potential
Trajectory
Wrong
model shows a test charge in an external electrostatic
potential and the associated electric field. The user can type
in an expression for the potential and see the (incorrect) trajectory
of the particle. Users
can examine and correct the model if
Ejs is
installed.
Exercises:
- Run
the simulation. The plot correctly shows the potential and electric
field. The initial potential: U(x,y)=1/(x*x+y*y)^(0.5) is the potential
due to a point charge at the origin. Explain how to get into the form
you are more familiar with. You can type new values of the potential as
a function of x
and y
in the input box and you can try new initial conditions. Even though
the plot of the potential (and equipotential contours) as well as the
electric field vectors are correct, the trajectory of the yellow
charged test particle*
is incorrect. Push the reset button and then play it and
observe what happens with the initial conditions. What should happen?
Why?
- If you need help, click on
the Hint
which shows a plot of kinetic and potential energy (correctly
calculated) for the particle. What is wrong? What is your
evidence? You may want to analyze the energy data using Data
Tool, the built-in data
analysis tool (click on the Wrench
button.):
- Once you think you know what
is going on, pick a different value for the potential (one in which you
know what should happen) and observe the trajectory and explain what is
wrong.
- What is wrong with this
simulation? What is your evidence?
- If you have EJS
installed, now that you have
determined what is wrong with the model, correct it. You will
need to go
to Model->Evolution
to make the
changes. Describe how you changed it and how you verified your work.
*Recall
that a test charge
is defined to feel the effects of an external electric field, but not
change the field itself (therefore, there are no field vectors around
it).
References:
- Giancoli, Physics
for Scientists and Engineers,
4th
edition, Chapter
23
(2008).
Credits:
The Electric Potential
Trajectory Wrong
Model
was
created by Wolfgang Christian 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/>.
