Name for 1/(4πε₀)? What is the Meaning?

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The constant 1/(4πε₀) is commonly referred to as the Coulomb constant, denoted as k, due to its appearance in Coulomb's Law. This constant arises from unit mismatches in the SI system and is related to the speed of light squared (c²). While ε₀ is often labeled as the permittivity of vacuum in elementary texts, its actual significance is not well-explained. Most physicists prefer using Gaussian units, where Coulomb's Law simplifies to V=q/r without the constant, and the factor of 4π originates from integrating the electric field over a sphere's surface area.

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Has a name been given to this constant? The most I've seen is calling it k, but is there another name for it, or any statement for understanding its meaning (such as how e0 can be called the "permittivity of vacuum")?
 
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It's called the Coulomb constant because it appears in Coulomb's Law.
 
The constant k appears because of a mismatch of units in the SI system.
It is related to c^2, but powers of ten come in because of the mismatch.
Gaussian units, in which V=q/r with no constant, is used by most working physicists in their own work. epsilon0 has nothing to do with the permittivity of free space, although all elementary texts do call it that, never with an explanation because there is none. Most graduate texts still use Gaussian units.
 
Couloumbs law is a special case of Gauss law. The factor of 4\pi is due to the integration of the electric field over the surface area of a sphere. In the more general Gauss law, only the factor of \epsilon_0 is present.

Claude.
 
The value of \epsilon_0 depends solely on the system of units used. The three most common systems used these days are the SI system, the Gaussian (or cgs) system, and the Heaviside-Lorentz (HL) system.
 

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