Principle

Superposition

F_{1} = i \neq = 1 \sum F_{i 1}

Statement

With several charges around, add the individual Coulomb forces as vectors.

Symbols and units

$F_{1}$	net force on charge 1	N
$F_{i 1}$	force from each other charge	N

When it applies

Linear media. Holds for forces, fields and potentials alike.

Derivation

Each pair interacts as if the others were absent, so write one Coulomb term per source charge:

F_{i 1} = k_{e} \frac{q _{i} q _{1}}{r _{i 1}^{2}} r_{i 1}

Add them as vectors — in practice, component by component:

F_{x} = i \sum F_{i 1, x}, F_{y} = i \sum F_{i 1, y}

Recombine into magnitude and direction at the end:

F = F_{x}^{2} + F_{y}^{2}, tan θ = \frac{F _{y}}{F _{x}}

Worked examples

Three collinear charges

+q at x = 0, +q at x = d, −q at x = 2d. Force on the middle charge:

F = k_{e} \frac{q ^{2}}{d ^{2}} + k_{e} \frac{q ^{2}}{d ^{2}} = \frac{2 k _{e} q ^{2}}{d ^{2}}

Repulsion from the left charge and attraction towards the right charge act in the same direction.

Watch out for

Never add magnitudes. And no charge can shield another: putting a third charge in between does not weaken the force between the first two (a conductor in between is a different story — its own charges rearrange).