Screen
shot of co-centric spheres (a) electric field and (b) equipotential.
Electric Field and Potential
Model
The EJS Electric Field and
Potential
Model shows the electric field and potential for cylindrical and
spherical symmetry. In both symmetries, there are co-centric charged
surfaces where the outer surface is grounded. The model reports the
force on a test charge (yellow) between the co-centric surfaces as well
as the
voltage. Information
about EJS is available at:
<http://www.um.es/fem/Ejs/>.
Exercises:
- Books often show
two-dimensional representations of electric field vectors. Notice, for
example, that the two-dimensional representation of co-centric
cylinders and co-centric spheres are the same:
Suppose you have a flat sheet of material with charged conductors.
Would you expect the electric field and potential to be more
like that of (a) sphere or (b) cylinder? Explain.
- Run the simulation. You can
zoom in (Shift-Click-Drag),
rotate (Click-Drag)
or pan (Ctrl-Click-Drag)
the 3D views. What are
the differences do you observe in the functional form of the electric
field vectors
between the
cylinder and sphere?
- How does the Equipotential Plot
change for the spherical
or cylindrical symmetry as you change z-location (moving
the
z-slider) of the plane? Explain.
- By clicking on a point in the Equipotential Plot,
you can measure the voltage. For z=0, how
does the voltage change as a function of distance from the center for
the cylinder? sphere?
- The simulation also shows a
test charge (yellow) with a force vector on
it. Move the test charge around. As you move the test charge, the
simulation records the position of the test charge (in cm)
as well as the
force (in 10-12
N). If the test charge has a charge of 1 pC (10-12
C), what is the linear charge density (for the long line of
charge) and the charge of the charged sphere?
References:
- Giancoli, Physics
for Scientists and Engineers,
4th
edition, Chapter 29
(2008).
Credits:
The Electric Field and
Potential Model was created by Anne J Cox
and modified by Wolfgang Christian using the Easy Java Simulations
(EJS) authoring and modeling
tool. Exercises 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/>.
