# Coulomb’s Law¶

*Coulomb’s law* describes the force between two points charges
(q_{2} on q_{1}):

where is the *electric constant*,
r is the distance between the two points, and
is a unit vector pointing in the direction from q_{2}
to q_{1}. Alternately it can be expressed in terms of electric field
():

Since forces (and electric fields) are additive, Coulomb’s law in theory
allows deriving the electric field from any distribution of charge in space.
In practice, the *Laplace Equation* or *Poisson Equation* are
often more useful for solving the electric field (and SIMION Refine uses them
for that).

One place where Coulomb’s law does come up in SIMION is in its charge
repulsion methods (see SIMION Example: repulsion and *Space Charge*)
to simulate things like ion-ion repulsions, ignoring interactions between ions
and electrode surface charges (which the *Poisson Equation* will fully
account for).

Observe that the electric potential from a point charge is proportional to 1/r, as seen by simply integrating Coulomb’s law:

Interestingly, a *spherical capacitor* also has a 1/r potential:
The sphere with uniform surface charge generates the same field as a single
point charge.

See also Wikipedia:Coulomb’s_law.