Based on the transmission line approximation, three different equivalent formulations have been proposed for evaluating the interaction between an external electromagnetic field and a transmission line. The difference among these 'coupling' formulations, which are summarized for the case of a lossless line, lies essentially in the representation of the source terms as a function of the external electromagnetic field components. In the paper we show that the contribution of a given electromagnetic field component is different depending on the particular adopted formulation. To show that, the three formulations are employed to calculate the voltages induced on an overhead line by a nearby lightning strike, and the contribution to the induced voltage of the various electromagnetic field components explicitly appearing in each formulation is emphasized. We conclude that it is misleading to speak about the contribution of a given electromagnetic field component to the total induced voltages without first specifying the coupling formulation one is using.