At the birthday party of your favorite (son, daughter, niece, nephew),
you have many balloons ready to play a game. While waiting to start a
game, everyone rubs a balloon on their heads, and they notice that if
they hold a balloon closer to a girl?s skirt, her skirt is lifted up
by the force pulling it toward the balloon. They wonder about this
?magic trick? then ask you how this can happen. You realize that you
can impress your friends and family about Electrostatic that you learn
at school.
     Knowing that the electrostatic can be induced by rubbing
materials together, you can assume that there is a net positive charge
of 4 µC(microcoulomb) on the balloon and a net negative charge of -4
nC(nanocoulomb) on the skirt. Next, you must set up a coordinate
system of both materials, assume that the balloon is located at (x =
1cm, y = 2 cm, z = 3 cm). You realize that the balloon must be as
close as 10 cm before you can see the movement on the skirt.

a) Choose the location of the skirt on the Cartesian coordinate so
that the distance between the skirt and the balloon is 10 cm. (More
than one locations will satisfy this situation, please pick only one
location to demonstrate your point to the kids).

b) What is the method you will use to find an Electric field that
induces the ?magical? force in this problem? Choose one (Coulomb?s
law, Gauss?s law, Electric Potential). Justify your answer.

c) Find the force (magnitude and direction) exerted on the skirt by
the balloon. Is this a large force? Note: unit Newton = Coulomb *
(Volt/meter).

d) Find the force (magnitude and direction) exerted on the balloon by the skirt. 

e) Explain this ?magical? force to the kids. Also, explain why the
force increases dramatically when the balloon is brought closer to the
skirt.

f) Find the electric field (magnitude and direction) at the origin
P(0,0,0) produced by the charge on the balloon. (Ignore the electric
field produced by the skirt).