While the Sense of Agency (SoA) has so far been predominantly characterised in VR as a component of the Sense of Embodiment, other communities (e.g., in psychology or neurosciences) have investigated the SoA from a different perspective proposing complementary theories. Yet, despite the acknowledged potential benefits of catching up with these theories a gap remains. This paper first aims to contribute to fill this gap by introducing a theory according to which the SoA can be divided into two components, the feeling and the judgment of agency, and relies on three principles, namely the principles of priority, exclusivity and consistency. We argue that this theory could provide insights on the factors influencing the SoA in VR systems. Second, we propose novel approaches to manipulate the SoA in controlled VR experiments (based on these three principles) as well as to measure the SoA, and more specifically its two components based on neurophysiological markers, using ElectroEncephaloGraphy (EEG). We claim that these approaches would enable us to deepen our understanding of the SoA in VR contexts. Finally, we validate these approaches in an experiment. Our results (N=24) suggest that our approach was successful in manipulating the SoA as the modulation of each of the three principles induced significant decreases of the SoA (measured using questionnaires). In addition, we recorded participants' EEG signals during the VR experiment, and neurophysiological markers of the SoA, potentially reflecting the feeling and judgment of agency specifically, were revealed. Our results also suggest that users' profile, more precisely their Locus of Control (LoC), influences their level of immersion and SoA.