Why we multiply charges in the coulomb's law equation

AI Thread Summary
The discussion centers on the rationale behind multiplying charges in Coulomb's law rather than adding them. Participants explore the relationship between charge magnitudes and the resulting force, emphasizing that multiplying charges aligns with intuitive expectations regarding force changes when altering charge quantities. The conversation also touches on the experimental basis of Coulomb's law, linking it to Maxwell's equations and the inverse square nature of the force. Additionally, there is a connection made between Coulomb's law and Newton's third law, suggesting that the mutual force exerted by two charges justifies the multiplication of their values. Ultimately, the consensus is that the multiplication of charges is necessary to maintain consistency with observed physical laws.
jonah.seler
Messages
8
Reaction score
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.
 
Physics news on Phys.org
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:
 
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
 
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:
 
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:
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Back
Top