State the relationship between the induced EMF $V$ in a loop and the flux $\Phi$ through it. State the force law for a current-carrying wire in a magnetic field $\mathbf{B}$.

A rectangular loop of wire with mass $m$, width $w$, vertical length $l$, and resistance $R$ falls out of a magnetic field under the influence of gravity. The magnetic field is $\mathbf{B}=B \hat{\mathbf{x}}$ for $z \geqslant 0$ and $\mathbf{B}=0$ for $z<0$, where $B$ is constant. Suppose the loop lies in the $(y, z)$ plane, with its top initially at $z=z_{0}<l$. Find the equation of motion for the loop and its terminal velocity, assuming that the loop continues to intersect the plane $z=0$.