Ionic liquids (ILs) are promising electrolytes for electrochemical applications due to their remarkable stability and high charge density. Molecular dynamics simulations are essential for a better understanding of the complex phenomena occurring at the electrode-IL interface. In this work, we have studied the interface between graphene and 1-ethyl-3-methyl-imidazolium tetrafluoroborate IL by density functional theory-based molecular dynamics (DFT-MD) simulations at variable surface charge densities. We have disassembled the electrical double layer potential drop into two main components: one involving atomic charges and the other dipoles. The former component arises due to the reorganization of ionic liquid and the latter due to the electronic polarization of the surface. It is related to concepts hotly debated in the literature, such as the Thomas-Fermi screening length, effective surface charge plane, and quantum capacitance.