We study, using Rindler coordinates, the quantization of a charged scalar field interacting with a constant (Poincare invariant), external, electric field in (1+1) dimensionnal flatspace: our main motivation is pedagogy. We illustrate in this framework the equivalence between various approaches to field quantization commonly used in the framework of curved backgrounds. First we establish the expression of the Schwinger vacuum decay rate, using the operator formalism. Then we rederive it in the framework of the Feynman path integral method. Our analysis reinforces the conjecture which identifies the zero winding sector of the Minkowski propagator with the Rindler propagator. Moreover, we compute the expression of the Unruh's modes that allow us to make a connection between the Minkowskian and Rindlerian quantization schemes by purely algebraic relations. We use these modes to study the physics of a charged two level detector moving in an electric field whose transitions are due to the exchange of charged quanta. In the limit where the Schwinger pair production mechanism of the exchanged quanta becomes negligible we recover the Boltzman equilibrium ratio for the population of the levels of the detector. Finally we explicitly show how the detector can be taken as the large mass and charge limit of an interacting fields system.