A system of n discrete charges q i stationed at r i = r − − r i produces an electric field whose magnitude and direction is, by superposition E ( r ) = 1 4 π π ε ε 0 ∑ ∑ i = 1 n q i r ^ ^ i | r i | 2 = 1 4 π π ε ε 0 ∑ ∑ i = 1 n q i r i | r i | 3