Why we multiply charges in the coulomb's law equation

In summary, the force between two charges is proportional to the charges, but we also multiply the charges to get a bigger force.
  • #1
jonah.seler
8
0
Hi.I want to know why we multiply the separate charges in the coulomb equation.I understand that the force is proportional to the charges, but I don't understand why we multiply charges.Why just we don't add them together.Are there any theoretical explanation for this.The same goes for the Gravitational law.I need some theoretical explanation in the form of the Newton laws.
 
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  • #2
hi jonah! :smile:

suppose you replaced one of the charges by ten charges equal to it …

wouldn't you expect the force to be multiplied by ten (not 5.5)? :wink:
 
  • #3
Hi Tiny Tim.I'm afraid I don't understanding.If I replace one of the charges with ten more I know that the force would be 10 times bigger.But that, the formula says.But I want to have some intuitive understanding of this.
Other man told me that Coulomb law is a direct consequence of Maxwells equations particularly Gauss' law so it is an experimental fact and you cannot get intuitive understanding of it.It just the way it is.
I don't know if this is true.Thank Tiny tim
 
  • #4
hi jonah! :smile:
jonah.seler said:
Other man told me that Coulomb law is a direct consequence of Maxwells equations particularly Gauss' law so it is an experimental fact and you cannot get intuitive understanding of it.It just the way it is.
I don't know if this is true.Thank Tiny tim

he's talking about the 1/r2 part of coulomb's law …

yes, that is experimental

(but the intuitive understanding is easy …

it's 1/r2 for the same reason that brightness from a point source is 1/r2

you have the same amount of power passing through a sphere at any distance! :wink:)

however, you were asking about the q1q2 part of coulomb's law …​
jonah.seler said:
Hi.I want to know why we multiply the separate charges in the coulomb equation.I understand that the force is proportional to the charges, but I don't understand why we multiply charges.Why just we don't add them together.

as you say …
If I replace one of the charges with ten more I know that the force would be 10 times bigger.But that, the formula says.But I want to have some intuitive understanding of this.

… but if you added the charges instead of multiplying them, that intuitive rule wouldn't work, would it? :wink:

you need to satisfy yourself that multiplying is the only way to achieve your intuitive rule :smile:
 
  • #5
I understand the "1/r2" part of the equation.The inverse square law is easy to understand.I have problem with the q1q2 part of coulomb's law,but I guess it experimental thing.
I don't understand one thing.Charles Coulomb was probably sure of his law because Coulomb had the torsion balance.But how Newton was sure for the M1M2.Cavendish with experiment tested the law years later.
I am probably wrong but I think that q1q2 and m1m2 are somehow related to the Newton third law.So when the first charge no matter how big it is in compassion to the second, exerts a force on the second charge,the second charge exerts that same force on the first and that is why we multiply them.
 
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1. Why do we use multiplication instead of addition in the coulomb's law equation?

The use of multiplication in the coulomb's law equation is necessary because it takes into account the magnitude of the two charges involved. Addition would not accurately represent the relationship between two charges, as the resulting force would not be proportional to the product of the two charges.

2. What is the significance of multiplying charges by the inverse square of the distance in the coulomb's law equation?

Multiplying charges by the inverse square of the distance in the coulomb's law equation takes into account the fact that the force between two charges decreases as the distance between them increases. This relationship is known as the inverse square law and is a fundamental principle in the field of electromagnetism.

3. Can you explain the physical meaning behind multiplying charges in the coulomb's law equation?

Multiplying charges in the coulomb's law equation represents the strength of the electric force between two charged objects. The larger the magnitude of the charges, the stronger the force between them. It also takes into account the distance between the charges, as the force decreases as the distance increases.

4. How does multiplying charges in the coulomb's law equation relate to the concept of electric fields?

The electric field is a vector quantity that represents the force experienced by a charged object placed in the field. The strength of the electric field is directly proportional to the magnitude of the charge that created it, and the distance from the charge. Multiplying charges in the coulomb's law equation is a way to mathematically express this relationship.

5. What happens if we do not multiply charges in the coulomb's law equation?

If we do not multiply charges in the coulomb's law equation, we would not accurately represent the relationship between two charges. The resulting force would not be proportional to the product of the two charges, and the concept of the inverse square law would not be taken into account. This would lead to incorrect calculations and a misunderstanding of the behavior of charged particles.

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