What is K called in Coulombs law?

"When man wanted to make a machine that would walk he created the wheel, which does not resemble a leg"

• The magnitude of the force of attraction (or repulsion), F12 between two point charges q1 and q 2  is given by Coulomb's Law.








where R12  is the distance between the charges.  k is a constant of proportionality known as the Coulomb constant, having the value 9 x 109  N.m2 / C2  in a vacuum. 


Note that the Coulomb constant, k, is often replaced with (1/4π ε0), where ε0is the permittivity of the vacuum (more later).

• The direction of this force is along the line joining the two charges with the sense determined by the relative signs of the charges

• Note that the force on each charge has the same magnitude (as required by Newton's third law of motion).

 
• For two 1 Coulomb charges separated by 1 metre the magnitude of the force is given by,
  F = (9 x 109  x 1 x 1 )/ 1  =  9 x 109   Newtons

  This is an extremely large force (sufficient to move Mt. Everest with an acceleration of 1cm/s2).  The Coulomb is a very large unit.  Typical macroscopic charges are measured in micro-coulombs (10-6 C).

• To handle situations with more than one charge, the charges must be treated in pairs, so that the overall force on one charge will be the

  vector

  sum of the force due to each of the other charges.  For example the force on q1 due to all other charges q2, q3 , q4... would be given by,

F1 = F21 + F31 + F41 + ...

• 
  Notice the similarity of Coulomb's Law to Newton's Law of Gravitation

both are "inverse square" laws.  Substitute charge for mass and "k" for "G" and you have Coulomb's law.

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Proportionality constant in electrodynamics equations

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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 base 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.[2][3]

Value of the constant

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

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

where êr is a unit vector in the r-direction.[4] In SI:

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

where ε 0 {\displaystyle \varepsilon _{0}}

S {\displaystyle {\scriptstyle S}}

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

Taking this integral for a sphere, radius r, centered 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.

S {\displaystyle {\scriptstyle S}} E ⋅ d A = | E | ∫ S d A = | E | × 4 π r 2 {\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,

F = 1 4 π ε 0 Q q r 2 e ^ r = k e Q q r 2 e ^ r ∴ k e = 1 4 π ε 0 {\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}}}

Coulomb's law is an inverse-square law, and thereby similar to many other scientific laws ranging from gravitational pull to light attenuation. This law states that a specified physical quantity is inversely proportional to the square of the distance.

intensity = 1 d 2 {\displaystyle {\text{intensity}}={\frac {1}{d^{2}}}}

k e = 1 4 π ε 0 = c 2 μ 0 4 π = c 2 × ( 10 − 7   H ⋅ m − 1 ) = 8.987   551   787   368   1764 × 10 9   N ⋅ m 2 ⋅ C − 2 . {\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,[6][7] 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]

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

Use

The Coulomb constant is used in many electric equations, although it is sometimes expressed as the following product of the vacuum permittivity constant:

k e = 1 4 π ε 0 . {\displaystyle k_{\text{e}}={\frac {1}{4\pi \varepsilon _{0}}}.}

The Coulomb constant appears in many expressions including the following:

F = k e Q q r 2 e ^ r . {\displaystyle \mathbf {F} =k_{\text{e}}{Qq \over r^{2}}\mathbf {\hat {e}} _{r}.}

U E ( r ) = k e Q q r . {\displaystyle U_{\text{E}}(r)=k_{\text{e}}{\frac {Qq}{r}}.}

E = k e ∑ i = 1 N Q i r i 2 r ^ i . {\displaystyle \mathbf {E} =k_{\text{e}}\sum _{i=1}^{N}{\frac {Q_{i}}{r_{i}^{2}}}\mathbf {\hat {r}} _{i}.}

See also

• Gravitational constant
• Vacuum permittivity
• Vacuum permeability
• Inverse-square law

References

1. ^ a b Derived from ke = 1/(4πε0) – "2018 CODATA Value: vacuum electric permittivity". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
2. ^ Britannica, The Editors of Encyclopaedia. "Coulomb". Encyclopedia Britannica. Retrieved 3 March 2021. {{cite web}}: |last1= has generic name (help)
3. ^ Britannica, The Editors of Encyclopaedia. "Charles-Augustin de Coulomb". Encyclopedia Britannica. Retrieved 3 March 2021. {{cite web}}: |last1= has generic name (help)
4. ^ Tomilin, K. (1999). "Fine-structure constant and dimension analysis". European Journal of Physics. 20 (5): L39–L40. Bibcode:1999EJPh...20L..39T. doi:10.1088/0143-0807/20/5/404. S2CID 250841835.
5. ^ Coulomb's constant, HyperPhysics
6. ^ BIPM statement: Information for users about the proposed revision of the SI (PDF)
7. ^ "Decision CIPM/105-13 (October 2016)". The day is the 144th anniversary of the Metre Convention.

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