# k

Charles-Augustin de Coulomb's Force Constant

Coulomb's electrical force constant has remained unknown and undefined for 200 years.

The following is a mathematical description of its true and accurate values and units

**k = mₑ.c².rₙ/e² = 8.98755184732667E+09 kg.m³ / C².s² per metre**

k is therefore a factor

## The Mathematical Explanation

You will see the units for this constant (k) written as: N.m²/C², which were units of convenience originally assigned to reflect Coulomb's formula:

F = k.q₁.q₂ / R²

This was because the formula for 'k' was unknown, hence its units were also unknown.

'k' is Coulomb's constant equivalent to Isaac Newton's gravitational constant 'G' and is used to calculate attractive electrical force in exactly the same fashion. I.e.:

Isaac Newton's formula for gravitational force:

F = G.m₁.m₂ / R²

Charles-Augustin de Coulomb's formula for electrical force:

F = k.q₁.q₂ / R²

The difference between the two is defined as the coupling ratio:

φ = G.mₚ.mₑ / k.qₚ.qₑ = 4.40742111792335E-40

Coulomb's constant (k) is used in his force formula:

k = μₒ.c² / 4.π = 8.98755184732667E+09 kg.m³ / s².C²

k = σ.c² kg.m³ / s².C²

where:

mₑ = mass of an electron

q₁ = q₂ = e

μₒ = 4.π / 1E+07 H/m

σ = μₒ / 4.π kg.m/C²

σ = 1E-07 = mₑ.rₙ/e² kg.m/C²

rₙ = neutronic radius (2.817937953839E-15 m)

c = 299792459 m/s

k = mₑ.c².rₙ/e² kg.m³ / C².s²

Like Newton's 'G', Coulomb's 'k' is a also a factor, therefore;

k = mₑ.c².rₙ/e² kg.m³ / C².s² per metre

### Further Reading

You will find further reading on this subject in reference publications^{(68, 69, & 70)}

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