 Resistive magnetic entry of a falling loop

A rectangular loop entering a uniform magnetic field while only one horizontal segment is immersed has motional electromotive force $Bav$. Neglecting self-inductance, its electric current is $Bav/R$ and its upward magnetic force is $(Ba{)}^{2}v/R$. The equation $m\dot{v}=mg-(Ba{)}^{2}v/R$ gives exponential relaxation toward $mgR/(Ba{)}^2$. This entry model ends when both horizontal segments enter the field; then their net magnetic force and the rate of change of external magnetic flux vanish.