Question

In Coulombers law in
electrostatics, what is
the S.I. Unit of
proportionality constant?​

Answer 1

Answer:

I think so k and it is dependent on medium

Answer 2

Answer:

Value of kUnits8.9875517923(14)×109N·m2/C214.3996eV·Å·e−210−7(N·s2/C2)c2

The Coulomb constant, the electric force constant, or the electrostatic constant (denoted ke, k or K) is a proportionality constant in electrostatics equations. In SI units it is equal to 8.9875517923(14)×109 kg⋅m3⋅s−4⋅A−2.[1] It was named after the French physicist Charles-Augustin de Coulomb (1736–1806) who introduced Coulomb's law.

Value of the constantEdit

The Coulomb constant is the constant of proportionality in Coulomb's law,

{\displaystyle \mathbf {F} =k_{\text{e}}{\frac {Qq}{r^{2}}}\mathbf {\hat {e}} _{r}}

where êr is a unit vector in the r-direction.[2] In SI:

{\displaystyle k_{\text{e}}={\frac {1}{4\pi \varepsilon _{0}}},}

where {\displaystyle \varepsilon _{0}} is the vacuum permittivity. This formula can be derived from Gauss' law,

{\displaystyle {\scriptstyle S}} {\displaystyle \mathbf {E} \cdot {\rm {d}}\mathbf {A} ={\frac {Q}{\varepsilon _{0}}}}

Taking this integral for a sphere, radius r, centred on a point charge, the electric field points radially outwards and is normal to a differential surface element on the sphere with constant magnitude for all points on the sphere.

{\displaystyle {\scriptstyle S}} {\displaystyle \mathbf {E} \cdot {\rm {d}}\mathbf {A} =|\mathbf {E} |\int _{S}dA=|\mathbf {E} |\times 4\pi r^{2}}

Noting that E = F/q for some test charge q,

{\displaystyle {\begin{aligned}\mathbf {F} &={\frac {1}{4\pi \varepsilon _{0}}}{\frac {Qq}{r^{2}}}\mathbf {\hat {e}} _{r}=k_{\text{e}}{\frac {Qq}{r^{2}}}\mathbf {\hat {e}} _{r}\\[8pt]\therefore k_{\text{e}}&={\frac {1}{4\pi \varepsilon _{0}}}\end{aligned}}}

In some modern systems of units, the Coulomb constant ke has an exact numeric value; in Gaussian units ke = 1, in Lorentz–Heaviside units (also called rationalized) ke = 1/4π. This was previously true in SI when the vacuum permeability was defined as μ0 = 4π×10−7 H⋅m−1. Together with the speed of light in vacuum c, defined as 299792458 m/s, the vacuum permittivity ε0 can be written as 1/μ0c2, which gave an exact value of[3]

{\displaystyle {\begin{aligned}k_{\text{e}}={\frac {1}{4\pi \varepsilon _{0}}}={\frac {c^{2}\mu _{0}}{4\pi }}&=c^{2}\times (10^{-7}\ \mathrm {H{\cdot }m} ^{-1})\\&=8.987\ 551\ 787\ 368\ 1764\times 10^{9}~\mathrm {N{\cdot }m^{2}{\cdot }C^{-2}} .\end{aligned}}}

Since the redefinition of SI base units,[4][5] the Coulomb constant is no longer exactly defined and is subject to the measurement error in the fine structure constant, as calculated from CODATA 2018 recommended values being[1]

{\displaystyle k_{\text{e}}=8.987\,551\,7923\,(14)\times 10^{9}\;\mathrm {kg{\cdot }m^{3}{\cdot }s^{-4}{\cdot }A^{-2}} .}

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