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 cm2, whereas the one on the right only has a charge of 4 units of charge per 6 cm2.

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 cm2.

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 1018 cm2. 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.

# Example

Two spheres are in contact with one another. Each originally has the same charge. But one of the spheres is smaller (area = 9 cm2), so it loses 4 units of charge to the less crowded and larger sphere (area = 18 cm2).

How many units of charge did each sphere begin with?

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

x = 12

## Coulomb’s Law

(430 only) The force, F, between two objects with charge q1 and q2, is given by:

, where r = distance between the two charges in meters

k = Coulomb's constant = 9 X 109 Nm2/C2.

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)-1]2 = 4.

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 q1 with 2q1?

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.