The field created by a charge

Rather than speaking of the force between two charges, we can say that a charge Q modifies the space around it: it creates an electric field there. A second charge q, placed at a point, does not "see" Q directly — it only feels the field present where it sits.

The field created by a point charge Q at distance r follows directly from Coulomb's law:

   E = k · |Q| / r²        (the field, in volts per metre)
   F = q · E               (the force felt by a charge q placed in this field)

The field too decreases as 1/r². It is pictured with field lines, which leave positive charges and enter negative ones:

      charge +                    charge −
       \  |  /                     /  |  \
     <-- (+) -->                 --> (−) <--
       /  |  \                     \  |  /
   (lines flee from +)          (lines plunge toward −)

Where the lines crowd together, the field is intense; where they spread out, it is weak. The value of this notion is immense: once the field is known at a point, the force on any charge q placed there is simply F = qE. We thus separate the cause (Q creating the field) from the effect (q feeling it). It is this idea of a field, born from Coulomb's law, that structures all of electromagnetism.