We present a new model for the topology of magnetic clouds at 1 AU that relates the magnetic field vector with the current density of the cloud without assuming the force-free condition. In addition, the model is formulated in such a way that it can be fitted directly to the data without the need of initially determining the flux rope axis by minimum variance. The model provides both the magnetic field strength and the direction in just one fitting procedure. In addition to the orientation of its axis and the relative closest-approach distance between the spacecraft and the cloud axis, the fit of the model to the experimental data allows an estimation of the current density of plasma inside the magnetic cloud. From our study on several clouds we conclude that this has values of the order of 10-12 C m-2 s-1. Compared with the force-free model, although the improvement gained in the χ2 values is not very great, the fitting procedure is shorter and easier, and the number of parameters involved has been reduced from seven to five. Our model also lets us check the validity of force-free approximation by the calculation of the value of the current density perpendicular to the flux rope, j⊥ = j ¿ B/|B|. This component is assumed to be zero in the force-free model, but for all analyzed cases we obtain a nonzero value. This finite value implies the existence of pressure gradients inside the cloud that cannot be explained with a force-free approximation. In this paper, four cases are presented that have already been analyzed in the literature. We show that our model can explain the profiles of the magnetic field as a magnetic cloud passes a spacecraft.