what do you mean by ' The net displacement is a vector addition of individual displacements.'?
This above is a definition of the classical field where charge is taken as continuous and non-quantized, to reflect the quantized nature of the field we cannot use the above definition but will have to resort to a definition of quantized field using quantum electrodynamics.
However, the above definition is very very accurate as well because e is very small charge and can be taken as “nearly zero” for macroscopic fields. Moreover, classical field (defined by the above definition) provides a basis for quantization of fields.