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Ke*q1*q2/r^2

Who was the first person (and when) to determine Ke?

How did they figure it out?

Who named it Coulomb's Constant?

- Thread starter Dr L
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- #1

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Ke*q1*q2/r^2

Who was the first person (and when) to determine Ke?

How did they figure it out?

Who named it Coulomb's Constant?

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This constant is simply a conversion factor from the units of charge to the mechanical units. In the SI it's [itex]K=\frac{1}{4 \pi \epsilon_0}[/itex]. In Gaussian units you have [itex]K=1[/itex] and in the rationalized Heaviside-Lorentz units, which in my opinion are the most naturla ones for theoretical E+M, [itex]K=\frac{1}{4 \pi}[/itex].

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Does anyone know who (and when) came up with the idea for Ke?

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http://en.wikipedia.org/wiki/Coulomb's_law

There, indeed they also call the constant, Coulomb's constant. I do not know, which convention of units Coulomb historically used, but I guess it's the static Coulomb, which has become part of the Gaussian system of measures, i.e., it defines the electric charge unit by Coulomb's Law in the form

[tex]|\vec{F}_{\text{estat}}|=\frac{q_1 q_2}{r^2}.[/tex]

This is no longer the most natural definition since nowadays, on the most fundamental level, we understand the electromagnetic field as defined by the relativistically covariant Lagrangian,

[tex]\mathscr{L}=-\frac{1}{4} F_{\mu \nu} F^{\mu \nu} + \frac{1}{c} j_{\mu} A^{\mu}.[/tex]

Here [itex]F_{\mu \nu}=\partial_{\mu} A_{\nu}-\partial_{\nu} A_{\mu}[/itex] is Faraday's tensor in terms of the electromagnetic four-vector potential. It includes the electric and magnetic field components, and Maxwell's equation in this convention then read

[tex]\vec{\nabla} \cdot \vec{E}=\rho, \quad \vec{\nabla} \times \vec{B}-\frac{1}{c} \frac{\partial \vec{E}}{\partial t}=\frac{1}{c} \vec{j}.[/tex]

The constraints that lead to the derivability of the electromagnetic field components from a vector potential, which read in the three-dimensional form

[tex]\vec{E}=-\frac{\partial \vec{A}}{c \partial t}-\vec{\nabla A^0}, \quad \vec{B}=\vec{\nabla} \times \vec{A},[/tex]

are given by the inhomogeneous Maxwell equations,

[tex]\vec{\nabla} \times \vec{E}+\frac{1}{c} \frac{\partial \vec{B}}{\partial t}=0, \quad \vec{\nabla} \cdot \vec{B}=0.[/tex]

In this interpretation the Coulomb Law reads

[tex]|\vec{F}_{\text{estat}}|=\frac{q_1 q_2}{4 \pi r^2}.[/tex]

This is close to the Gaussian units but here the factor [itex]4 \pi[/itex] appears in the solution of Maxwell's eqs. and not in the eqs. themselves. This is the Heaviside-Lorentz system of units and used in theoretical high-energy physics.

The SI is invented for everyday use in electrical engineering and experimental physics. For theoretical physics in the relativistically covariant formulation it's a bit inconvenient, but of course the physics doesn't change with the change of units.

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I am writing a historical book- so does anyone know when (or who) someone came up with the convention for Coulomb's constant?

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Great reply by vanhees71. Thanks for taking the time.

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No, sorry, I don't know how the convention arose.

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C=[itex]\sqrt{\mu_{0}\epsilon_{0}}[/itex] where [itex]\mu_{0}[/itex] is permeability of free space, defined as [itex] \ 4\pi\ \times\ 10^{-7}[/itex] and thus [itex]\epsilon_{0}[/itex] is well defined, κ[itex]_{e}[/itex] is[itex]\frac{1}{4\pi \epsilon_{0}}[/itex]. So if we know c from experiments we can know k with any amount of accuracy.

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And the speed of light is 3.0 x 10E+08 m/s ?

It can't be a coincidence can it?

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