The evolution in the plasma of a magnetic field that is fast-rising at the plasma boundary, and the simultaneous pushing of the plasma by that magnetic field, are studied for the case that a parallel magnetic field is present in the plasma. It is shown that initially the magnetic field propagates into the plasma in the form of a whistler wave. The magnetic field evolution is then governed by the Schrodinger equation for a free particle, as described in the previous simplified analysis [Phys. Fluids B 3, 1546 (1991)]. Later, the gas-dynamics shock propagation exceeds the magnetic field propagation. If the magnetic field in the plasma is initially oblique and not parallel, a quasiperpendicular fast (super-Alfvenic) shock propagates in the plasma, following a whistler precursor. The width of the current channel is on the scale of the ion skin depth.