## Part II: A. Ratio of Charges

*Please wait for the animation to
completely load.*

Two fixed charges and a dragable test charge are placed as shown **(position
is given in meters and force is given in newtons)**. The blue arrow
represents the force on the red test charge. The forces on the fixed charges are not shown.
You can examine the forces with the first fixed charge,
with the
second fixed charge, or with both fixed charges in place. Notice that the net force on the test charge is displayed in the
yellow message box when you have only one charge present but not when you have both charges present.
Restart.

Answer the following questions with both fixed charges in place.

- Determine the net force on the test charge at the point (3 m,4 m). To do
this, select first and read the force due to the "first" charge alone
(magnitude and direction). Next, do the same for the
second charge.
- Sketch the two vectors represented by the forces in the usual "head to
tail" vector addition picture and then give the resultant net force (this
requires some math).
- Determine the net force on the test charge at a point midway between the
two charges by first finding the midpoint and then measuring the magnitude of
the force due to each charge (first and
second) and also consider the direction.
- Is (are) there any point(s) where the net force on the test charge is zero? If so, find those
points. Check this by moving the charge, but also think about it.
How many such points are possible? Where should such "equilibrium" points be
located when the charges are the same? when the charges are opposite?
- What is the ratio of the charges? (First charge is lower right.)
Start with the test charge at the equilibrium point. Then, you will need
to use Coulomb's law and also determine the distance to the equilibrium point
from each charge. Also, what is the net force and the force due to each
charge on the test charge at that point?

Original problem: **Exploration 22.1 ***Physlet Physics* by Christian and Belloni

© 2004 by Prentice-Hall, Inc. A Pearson Company