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Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law [1] of physics that calculates the amount of force between two electrically charged particles at rest. This electric force is conventionally called the electrostatic force or Coulomb force . [ 2 ]
where r is the distance between the point charges q and Q, and q and Q are the charges (not the absolute values of the charges—i.e., an electron would have a negative value of charge when placed in the formula). The following outline of proof states the derivation from the definition of electric potential energy and Coulomb's law to this formula.
Notably, the electric potential due to an idealized point charge (proportional to 1 ⁄ r, with r the distance from the point charge) is continuous in all space except at the location of the point charge. Though electric field is not continuous across an idealized surface charge, it is not infinite at any point. Therefore, the electric ...
This situation is equivalent to the original setup, and so the force on the real charge can now be calculated with Coulomb's law between two point charges. [2] The potential at any point in space, due to these two point charges of charge +q at +a and −q at −a on the z-axis, is given in cylindrical coordinates as
The fundamental equation of electrostatics is Coulomb's law, which describes the electric force between two point charges. Another result, Earnshaw's theorem , states that a collection of point charges cannot be maintained in a static equilibrium configuration solely by the electrostatic interaction of the charges.
Strictly speaking, Gauss's law cannot be derived from Coulomb's law alone, since Coulomb's law gives the electric field due to an individual, electrostatic point charge only. However, Gauss's law can be proven from Coulomb's law if it is assumed, in addition, that the electric field obeys the superposition principle. The superposition principle ...
The coulomb was originally defined, using the latter definition of the ampere, as 1 A × 1 s. [4] The 2019 redefinition of the ampere and other SI base units fixed the numerical value of the elementary charge when expressed in coulombs and therefore fixed the value of the coulomb when expressed as a multiple of the fundamental charge.
The formula provides a natural generalization of the Coulomb's law for cases where the source charge is moving: = [′ ′ + ′ (′ ′) + ′] = ′ Here, and are the electric and magnetic fields respectively, is the electric charge, is the vacuum permittivity (electric field constant) and is the speed of light.