# Coulomb's Law

## The electric force acting on a point charge

Coulomb's law calculates the electric force acting between to electric charges *q _{1}* and

*q*

_{2}and can be expressed as

*F = k q _{1} q_{2} / r^{2} *

* = q _{1} q_{2} / (4 π ε_{0} r^{2}) (1)*

*where *

*F = force of attraction or repulsion (N)*

*k = Coulomb's constant = 1 / (4 π ε _{0}) = 8.9875517873681764 × 10^{9} (Nm^{2}/C^{2}) in air*

*q = charge (Coulombs, C)*

*r = distance between charges (m)*

*ε _{0} = permittivity of space or vacuum*

_{}

The **quantity of charge** (number of electrons) is measured in the unit Coulomb - *C - *where

1 coulomb (C) = 6.24 10^{18}electrons

The smallest charge that exists is the charge carried by an electron equal to *-1.602 10 ^{-19} coulomb*.

### Example - Force between two Charged Bodies

Two spheres in air with distance *20 mm* is both charged with *2 μC (2 10 ^{-6} C)*. The force acting between the two spheres can be calculated as

*F = ( 8.98755 10^{9} Nm^{2}/C^{2}) ((2 μC) (10^{-6} C/μC)) ((2 μC) (10^{-6} C/μC)) / ((20 mm)(10^{-3} m/mm))^{2}*

* = 90 N*

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