# Value of Charge Q: Why Use Distance not Radius?

• random_user13
In summary, the conversation is discussing problem 1.4 from Purcell's Electricity and Magnetism 2nd edition, which involves two volleyballs tethered by nylon strings and charged by an electrostatic generator. The question is about finding the charge on each ball, assuming they are equal, with given values of height and distance between the charges. The conversation also touches on confusion about using radius or distance between the charges in the calculation of electrostatic force.
random_user13

## Homework Statement

this is problem 1.4 from purcells electricity and magnetism 2nd edition.

Two volleyballs, mass 0.3 kg each, tethered by nylon strings and charged by an electrostatic generator, hang as shown in the diagram. which cam be found here http://www.fysik.su.se/grulab//LabDataBas/2005/2005_9_27_14_21_10/R1_03.pdf
the height is 2.5 m and distance between the charges 0.5 m the diagram is a little messed up.
What is the charge on each in coulombs assuming the charges are equal? When trying to work this problem, I ended up just looking up the solution online here. i was getting close to the answer. I used the radius instead pf the distance between the two charges. Hence my question:

I don't understand why the distance between the two charges is used. Should the radius not be used?

random_user13 said:
I don't understand why the distance between the two charges is used. Should the radius not be used?
Used for what? For finding the electrostatic force between them? And by radius you mean the length of of the string?

Radius is the same thing as distance. In Coulomb's force equation, radius refers to the distance between the two point charges, not half the distance (like the definition of radius you are thinking).

That makes sense now. Definitely mixed up how that was being used.

## 1. What is the value of charge Q?

The value of charge Q refers to the amount of electric charge that an object possesses. It is measured in coulombs (C).

## 2. Why is distance used instead of radius when talking about the value of charge Q?

Distance is used instead of radius because electric charge is a property of point-like particles, meaning they have no physical size or volume. Therefore, it is more accurate to use the distance between the charges rather than the radius of the particles to calculate the value of charge Q.

## 3. How is the distance between charges determined?

The distance between charges is determined by measuring the distance between the centers of the two objects or particles that are carrying the charges.

## 4. Can the value of charge Q change depending on the distance between charges?

Yes, the value of charge Q can change depending on the distance between charges. According to Coulomb's Law, the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This means that as the distance between the charges increases, the value of charge Q will decrease.

## 5. Why is it important to consider distance when calculating the value of charge Q?

It is important to consider distance when calculating the value of charge Q because it directly affects the strength of the electric force between two charges. Without taking distance into account, the calculated value of charge Q may not accurately represent the true strength of the electric force between the charges.

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