We study the magnetic field and current structure associated with a coronal loop. Through this we investigate to what extent the assumptions of a force-free magnetic field break down. We analyse a three-dimensional MHD model of the solar corona in an emerging active region with the focus on the structure of the forming coronal loops. The lower boundary of this simulation is taken from a model of an emerging active region. As a consequence of the emerging magnetic flux a coronal loop formes self-consistently. We investigate the current density along magnetic field lines inside (and outside) this loop and study the magnetic and plasma properties in and around this loop. The loop is defined as the bundle of field lines that coincides with enhanced emission in extreme UV. We find that the total current along the emerging loop changes its sign from being antiparallel to parallel to the magnetic field. Around the loop the currents form a complex non-force-free helical structure. This is directly related to a bipolar currents at the loop footpoints at the base of the corona and a local reduction of the background magnetic field (i.e. outside the loop) caused by the plasma flow into and along the loop. Furthermore, the locally reduced magnetic pressure in the loop allows to sustain a higher density, which is crucial for the emission in extreme UV. The acting of the flow on the magnetic field hosting the loop turns out to be also responsible for the observed squashing of the loop. The complex magnetic field and current system surrounding it can be modeled only in three-dimensional MHD models where the magnetic field has to balance the plasma pressure. A one-dimensional coronal loop model or a force-free extrapolation can not capture the current system and the complex interaction of the plasma and the magnetic field in the loop, despite the fact that the loop is under low-$β$ conditions. ; Comment: 10 pages, 11 figures, submitted to A&A