Coulomb constant: Difference between revisions
DominicPrice (talk | contribs) →Value of the constant: Added a small derivation to explain where the value comes from |
DominicPrice (talk | contribs) →Use of Coulomb's constant: Coulomb's law was written in a bizarre way |
||
Line 40: | Line 40: | ||
[[Coulomb's law]]: |
[[Coulomb's law]]: |
||
:<math> |
:<math>\mathbf{F}=k_\text{e}{Qq\over r^2}\mathbf{\hat{e}}_r</math>. |
||
[[Electric potential energy]]: |
[[Electric potential energy]]: |
||
:<math> U_\text{E}(r) = k_\text{e}\frac{ |
:<math> U_\text{E}(r) = k_\text{e}\frac{Qq}{r}</math>. |
||
[[Electric field]]: |
[[Electric field]]: |
Revision as of 13:02, 3 May 2014
Coulomb's constant, the electric force constant, or the electrostatic constant (denoted ke ) is a proportionality constant in equations relating electric variables and is exactly equal to ke = 8.9875517873681764×109 N·m2/C2 (m/F). It was named after the French physicist Charles-Augustin de Coulomb (1736–1806).
Value of the constant
Coulomb's constant can be empirically derived as the constant of proportionality in Coulomb's law,
where êr is a unit vector in the r direction. However, its theoretical value can be derived from Gauss' law,
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.
Noting that E = F/Q for some test charge Q,
This exact value of Coulomb's constant ke comes from three of the fundamental, invariant quantities that define free space in the SI system: the speed of light c0 , magnetic permeability μ0 , and electric permittivity ε0 , related by Maxwell as:
Because of the way the SI base unit system made the natural units for electromagnetism, the speed of light in vacuum c0 is 299792458 m s−1, the magnetic permeability μ0 of free space is 4π·10−7 H m−1, and the electric permittivity ε0 of free space is 1 ⁄ (μ0 c2
0 ) ≈ 8.85418782×10 −12 F m−1,[1]
so that[2]
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:
- .
Some examples of use of Coulomb's constant are the following:
- .
- .
- .
See also
References
- ^ CODATA Value: electric constant. Physics.nist.gov. Retrieved on 2010-09-28.
- ^ Coulomb's constant, Hyperphysics