Abstract. The ionosphere forms the inner boundary of near-Earth space, where collisionless space plasma transitions into a partially ionized gas that interacts with the neutral atmosphere through collisions. Conventional models for magnetosphere-ionosphere (MI) coupling use an electric circuit framework, where an electric potential is calculated from the current continuity equation on a thin spherical shell that represents the ionosphere. This approach, founded in the E, j (electric field and current density) paradigm, contrasts with the approach used to study plasmas in other regions of cosmos, where the magnetic field B and plasma velocity v are treated as fundamental variables (the B, v paradigm). Since traditional MI coupling models also neglect induction by setting ∂B/∂t = 0, they omit the dynamic processes by which B evolves, leaving the global MI coupling process arguably poorly understood. To advance our understanding of MI coupling, we present a new global model of the 2D ionosphere that incorporates induction, with B as the primary variable. This model accommodates arbitrary ionospheric conductance, neutral wind patterns, and realistic main magnetic field geometries. Simulations reveal the complex nature of the induction process over a few seconds to several minutes. The induction timescales depend on the magnitudes and spatial scales of conductance, neutral wind, imposed magnetic field perturbations, and main magnetic field geometry. We simulate for the first time how low-latitude Sq currents and electric fields emerge through induction. Our model has the potential to replace existing MI coupling modules in magnetospheric simulation codes, offering both a truly global solution, and the inclusion of induction in the coupled system dynamics.