Electric field
Superposition principle

Due to the linearity of Maxwell's equations, electric fields satisfy the superposition principle, which states that the total electric field, at a point, due to a collection of charges is equal to the vector sum of the electric fields at that point due to the individual charges. This principle is useful in calculating the field created by multiple point charges. If charges q 1, q 2, …, q n {\displaystyle q_{1},q_{2},\dots,q_{n}} are stationary in space at points r 1, r 2, …, r n {\displaystyle \mathbf {r} _{1},\mathbf {r} _{2},\dots,\mathbf {r} _{n}}, in the absence of currents, the superposition principle says that the resulting field is the sum of fields generated by each particle as described by Coulomb's law: E (r) = E 1 (r) + E 2 (r) + ⋯ + E n (r) = 1 4 π ε 0 ∑ i = 1 n q i r ^ i | r i | 2 = 1 4 π ε 0 ∑ i = 1 n q i r i | r i | 3 {\displaystyle {\begin{aligned}\mathbf {E} (\mathbf {r})=\mathbf {E} _{1}(\mathbf {r})+\mathbf {E} _{2}(\mathbf {r})+\dots +\mathbf {E} _{n}(\mathbf {r})={1 \over 4\pi \varepsilon _{0}}\sum _{i=1}^{n}q_{i}{{\hat {\mathbf {r} }}_{i} \over {|\mathbf {r} _{i}|}^{2}}={1 \over 4\pi \varepsilon _{0}}\sum _{i=1}^{n}q_{i}{\mathbf {r} _{i} \over {|\mathbf {r} _{i}|}^{3}}\end{aligned}}} where
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