Coulomb's law

In 1785, Charles-Augustin de Coulomb precisely measured this force using a torsion balance. The result, Coulomb's law, gives the intensity of the force between two point charges q₁ and q₂ separated by a distance r:

   F = k · |q₁ · q₂| / r²      (k ≈ 9 x 10^9 N·m²/C²)

Three lessons. The force is proportional to the product of the charges: doubling one charge doubles the force. It is inversely proportional to the square of the distance: it is a "1/r²" law, like gravitation. And the constant k measures the strength of the interaction in vacuum.

The square in the denominator has striking effects: moving the charges apart makes the force fall very fast.

   distance r    2r     3r     4r
   force    F    F/4    F/9    F/16      (division by the square)

Multiplying the distance by 2 divides the force by 4; by 3, divides it by 9. The direction lies along the line joining the charges: repulsive if they have the same sign, attractive otherwise.

   q1(+) <---F   r   F---> q2(+)      repulsion
   q1(+)   F--->  r  <---F  q2(−)      attraction

This modest-looking law is the foundation of all of electrostatics. It states exactly with what force two charges speak to each other, according to their values and their separation.