# Coulomb's law

*see Coulomb's law at Schools Wikipedia*

**Coulomb's law**is an inverse-square law indicating the magnitude and direction of electrical force that one stationary, electrically charged substance of small volume (ideally, a point source) exerts on another.

When one is interested only in the magnitude of the force (and not in its direction), it may be easiest to consider a simplified, scalar version of the Law

F is the magnitude of the force exerted, measured in Newtons

*q*_{1} is the charge on one substance, measured in Coulombs

*q*_{2} is the charge on the other, also measured in Coulombs

*r* is the distance between them measured in metres

ε_{0} is a universal constant, the permittivity of vacuum

ε_{0} ≈ 8.854 × 10^{−12} Fm^{−1} or C^{2}N^{−1}m^{−2}

Note that 1/(μ_{0}ε_{0}) = c^{2} × 10^{-7}, where μ_{0} is the permeability of vacuum and c is the speed of light.)

Among other things, this formula says that the magnitude of the force is directly proportional to the magnitude of the charges of each substance and inversely proportional to the square of the distance between them.

The force F acts on the line connecting the two charged objects.

For calculating the direction and magnitude of the force simultaneously, one will wish to consult the full-blown vector version of the Law

Since opposite charges attract, and like ones repel, when q_{1} and q_{2} are multiplied, it becomes easy to tell if the force is repulsive or attractive; when q_{1}q_{2} is negative, the force is attractive. When positive, the force is repulsive. (The r is not important because it always becomes 1)

(The r vector in the numerator indicates that the force should be along the vector connecting the two substances. |r| has been raised to the third power instead of the second in the denominator in order to normalize the length of the r in the numerator to 1.)

In either formulation, Coulomb's Law is fully accurate only when the substances are static (i.e. stationary), and remains approximately correct only for slow movement. When movement takes place, magnetic fields are produced that alter the force on the two substances. Especially when rapid movement takes place, the electric field will also undergo a transformation described by Einstein's theory of relativity.

## See also