### Induction

A rectangular wire frame with the length $a$ (in $x$ direction) and width $b$ ($y$ direction) is falling because of the gravity force $\mathbf{F}=mg\hat{y}$ in the magnetic field which is directed along $z$ and is inhomogeneous $B_z=B_0+\beta y$. Find the velocity of the frame as a function of time if it starts falling at $y=0$ and the resistance is $R$.