**Grounding**: is the process by which an object is allowed
to discharge (get rid of its excess charge).

(1)If
the object to be grounded is negatively charged, grounding lets excess
electrons to flow from the object into the earth or other large substance, or

(2) If the object is positively charged,
electrons flow from the earth or other large neutral substance into the object.

*On the left the picture shows
a charged electroscope, one that was charged by touching it with a balloon
which had been rubbed against a volunteer's hair. Notice how the leaves are
repelled ( looks like a butterfly). But when the leaves are touched the
electroscope is grounded. If the electroscope was stuck with a negative charge,
touching it allowed excess electrons to flow into the person's body.*

**Why Does
Grounding Happen?**

Grounding occurs because electrons repel
themselves and so will move from a crowded area (tip of lightning rod that’s
just been struck by lightning) to a non-crowded area such as the earth. Charge
density is a measure of just how crowded an area is.

** **

** **

** **

**Charge Density **

** **

What would happen if the two spheres were in
contact, given that the sphere eon the left has a charge density of 6 units per
6 cm^{2}, whereas the one on the right only has a charge of 4 units of
charge per 6 cm^{2}.

In theory, one unit of negative
charge should flow out of the crowded sphere and into the less crowded sphere.
At that point both spheres will have 5 units per 6 cm^{2}.

Now imagine the same sphere(the one with 6 units of charge
originally) in contact with the earth. What will happen to the charge? The
earth's area is 4.69 X 10^{18} cm^{2}. Even after losing 5
units of charge, it will still represent a higher charge density than the
earth. As a result, the last unit of charge will also leak into the earth. It
will be grounded.

Two spheres are in contact with one another.
Each originally has the same charge. But one of the spheres is smaller (area =
9 cm^{2}), so it loses 4 units of charge to the less crowded and larger
sphere (area = 18 cm^{2}).

How
many units of charge did each sphere begin with?

(x - 4)/9 = (x + 4)/18

x = 12

(430 only) The force, F, between two objects
with charge q_{1} and q_{2}, is given by:

, where
r = distance between the two charges in meters

k
= Coulomb's constant = 9 X 10^{9} Nm^{2}/C^{2}.

**Example
1**

(1)
By what factor would the attractive force between two oppositely-charged
objects increase if we decreased the distance between them to half of the
original distance?

Since
the force is ** inversely **proportional
to the square of the distance between the
charges, it will increase by a factor of
[(1/2)

**Example
1**

(2)
What would happen to the force of repulsion between two negatively-charged
objects if we doubled the distance between them and replaced q_{1} with
2q_{1}?

Force
is directly proportional to charge. So doubling charge doubles
the repulsive force, so far. But if we also double distance, the force becomes
[(2)^{-1}]^{2}
= ¼ of the original. The combined effect then
is a force that is ¼ * 2 =1/2 of the original
force.