Coulomb 's constant - wikipedia Coulomb 's constant This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. ( September 2016 ) Coulomb 's constant, the electric force constant, or the electrostatic constant ( denoted k, k or K ) is a proportionality constant in electrodynamics equations. In SI units, it is exactly equal to 7009898755178736817 ♠ 8987551787. 368 1764 N m C, or roughly equaling 7009899000000000000 ♠ 8.99 × 10 N m C. It was named after the French physicist Charles - Augustin de Coulomb ( 1736 -- 1806 ) who introduced Coulomb 's law. Contents 1 Value of the constant 2 Use of Coulomb 's constant 3 See also 4 References Value of the constant Coulomb 's 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 ê is a unit vector in the r - direction and k e = α ħ c e 2 ( displaystyle k_ ( \text ( e ) ) = alpha ( \frac ( hbar c ) ( e ^ ( 2 ) ) ) ), where α is the fine - structure constant, c is the speed of light, ħ is the reduced Planck constant, and e is elementary charge. 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 ) ) is the vacuum permittivity. This formula can be derived from Gauss ' law, 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, around a point charge, we note that the electric field points radially outwards at all times and is normal to a differential surface element on the sphere, and is constant for all points equidistant from the point charge. S ( displaystyle ( scriptstyle S ) ) E ⋅ d A = E e ^ r ∫ S d A = E e ^ r × 4 π r 2 ( displaystyle mathbf ( E ) cdot ( \rm ( d ) ) mathbf ( A ) = mathbf ( E ) mathbf ( hat ( e ) ) _ ( r ) int _ ( S ) dA = mathbf ( E ) mathbf ( hat ( e ) ) _ ( r ) \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 ) ) ) In modern systems of units Coulomb 's constant k is an exact constant, in Gaussian units k = 1, in Lorentz -- Heaviside units ( also called rationalized ) k = 1 / 4π and in SI k = 1 / 4πε, where the vacuum permittivity ε = 1 / μ c ≈ 6988885418782000000 ♠ 8.854 187 82 × 10 F m, the speed of light in vacuum c is 7008299792458000000 ♠ 299 792 458 m / s, the vacuum permeability μ is 4π × 10 H m, so that 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 m ) ^ ( - 1 ) ) & = 8.987 , 551 , 787 , 368 , 1764 \times 10 ^ ( 9 ) ~ mathrm ( N m ^ ( 2 ) C ^ ( - 2 ) ). end ( aligned ) ) ) Use of Coulomb 's constant Coulomb 's 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 ) ) ). ) Coulomb 's constant appears in many expressions including the following : Coulomb 's law : F = k e Q q r 2 e ^ r. ( displaystyle mathbf ( F ) = k_ ( \text ( e ) ) ( Qq over r ^ ( 2 ) ) mathbf ( hat ( e ) ) _ ( r ). ) Electric potential energy : U E ( r ) = k e Q q r. ( displaystyle U_ ( \text ( E ) ) ( r ) = k_ ( \text ( e ) ) ( \frac ( Qq ) ( r ) ). ) Electric field : 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 References Jump up ^ 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. Jump up ^ CODATA Value : electric constant. Physics.nist.gov. Retrieved on 2010 - 09 - 28. Jump up ^ Coulomb 's constant, Hyperphysics Retrieved from `` https://en.wikipedia.org/w/index.php?title=Coulomb%27s_constant&oldid=856074936 '' Categories : Electricity Electromagnetism Physical constants Hidden categories : Articles needing additional references from September 2016 All articles needing additional references Talk Contents About Wikipedia Español Հայերեն Bahasa Indonesia Italiano עברית Norsk Português Română Simple English 3 more Edit links This page was last edited on 22 August 2018, at 18 : 02 ( UTC ). About Wikipedia

Question: what is the k value in coulomb's law
Answer: Coulomb's constant