structural:scholar_edition, stylistic:style_transfer
System of discrete charges

The law of superposition allows Coulomb's law to be extended to include any number of point charges. The force acting on a point charge due to a system of point charges is simply the vector addition of the individual forces acting alone on that point charge due to each one of the charges. The resulting force vector is parallel to the electric field vector at that point, with that point charge removed.

Force F {\textstyle \mathbf {F} } on a small charge q {\displaystyle q} at position r {\displaystyle \mathbf {r} }, due to a system of n {\textstyle n} discrete charges in vacuum is

F (r) = q 4 π ε 0 ∑ i = 1 n q i r ^ i | r i | 2 = q 4 π ε 0 ∑ i = 1 n q i r i | r i | 3, {\displaystyle \mathbf {F} (\mathbf {r})={q \over 4\pi \varepsilon _{0}}\sum _{i=1}^{n}q_{i}{{\hat {\mathbf {r} }}_{i} \over {|\mathbf {r} _{i}|}^{2}}={q \over 4\pi \varepsilon _{0}}\sum _{i=1}^{n}q_{i}{\mathbf {r} _{i} \over {|\mathbf {r} _{i}|}^{3}},}

where q i {\displaystyle q_{i}} is the magnitude of the i th charge, r i {\textstyle \mathbf {r} _{i}} is the vector from its position to r {\displaystyle \mathbf {r} } and r ^ i {\textstyle {\hat {\mathbf {r} }}_{i}} is a unit vector in the direction of r i {\displaystyle \mathbf {r} _{i}}.