Proportionality Constant(k) In Coulomb's Law

[Cetullah]

Hello dear Physics Forums members,

My question is about the constant k, in Coulomb's law, which is:

1/4\pi ε0

Can anybody explain me where this constant comes from?

 

[DennisN]

Hi Cetullah! Absolutely - that is Coulomb's constant;

• Coulomb's Constant (HyperPhysics)
• Coulomb's Constant (ScienceWorld/Wolfram)
• Coulomb's Constant (Wikipedia)
  
• Coulomb's law (HyperPhysics/ScienceWorld/Wikipedia)

 

[Cetullah]

Thanks, I could access much more information when I Googled it as Coulomb Constant:

https://www.physicsforums.com/showthread.php?t=206172

 

[Cetullah]

Well, I think I started to get some things straight in my head. Well, I may have been using the wrong words, since my learning language is not English, but as I understand, it is about the electric flux. The density of the electric flux(which is electric field) decreases by the area of a mathematical spherical surface around the charge. So, it would make much sense if we wrote the formula as:

(1/4\piR²)*Q₁*Q₂/ε₀

which R is the distance between two charges, as we take it for the radius of the sphere, instead of d in the old Coulomb's law.

And of course, the whole force will be decreased if the electric permittivity(ε₀) increases, or the other way.

I hope I managed to tell you what I m thinking, and the way I settled it in my mind. Any critics, constructive ideas or other perspectives are welcome.

 

[DennisN]

Hi again, Cetullah! Generally, I'd say it's a good idea to mathematically group constants together like it's originally done in Coulomb's law, it makes it easier for the eye. The charges (q's) and the distance (r) are variables.

Regarding Coulomb's constant and why it is (1/4\piε₀):

Coulomb's law is related to Gauss's[/PLAIN] law. Here's some links for you:

• Gauss's Law (Doug Davis)
  
• http://planetmath.org/encyclopedia/CoulombsLaw.html (PlanetMath)
  
• Deriving Coulomb's law from Gauss's law (Wiki) (show Outline of proof)

 

[Cetullah]

Yeah, I got what you re saying ;) It just feels better when you get the logic tho :)