Homework Help: Why we multiply charges in the coulomb's law equation

1. Nov 15, 2012

jonah.seler

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.

2. Nov 15, 2012

tiny-tim

hi jonah!

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)?

3. Nov 16, 2012

jonah.seler

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. Nov 16, 2012

tiny-tim

hi jonah!
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! )

however, you were asking about the q1q2 part of coulomb's law …​
as you say …
… but if you added the charges instead of multiplying them, that intuitive rule wouldn't work, would it?

you need to satisfy yourself that multiplying is the only way to achieve your intuitive rule

5. Nov 16, 2012

jonah.seler

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.

Last edited: Nov 16, 2012