Top panel: magnitude of the magnetic field in our simulation from Fig. 1, with logarithmic color grading in code units, and poloidal magnetic field lines shown with white solid lines. In the middle part of the disk, the magnetic field is two orders of magnitude smaller than in the corona, as predicted by our analytical solution in the disk, where the zeroth-order field vanishes, B₀ = 0. The components are singled out in Fig. B.4. Near the boundaries, our analytical solution is less exact, as expected, since it is influenced by the magnetic field in the corona. Bottom panel: ratio of the gradient of magnetic pressure , which measures the magnetic force, to the sum of gas pressure gradient, centrifugal, and gravity forces, in logarithmic color grading. Inside the disk, and in particular in the middle part of the disk with r ∈ [5, 25]R_⋆, these other forces prevail over the magnetic ones.