Induced Currents and Magnetic Forces Practice Test

According to the scenario, a solenoid’s current ramps up, increasing magnetic flux through a nearby coil; Faraday’s Law $\mathcal{E}=-d\Phi/dt$ induces a current whose magnetic field opposes the increasing flux (Lenz’s Law), as in transformer action. According to Faraday's Law, what happens to the induced EMF when the magnetic field changes?

Based on the description, a metal rod of length $L$ moves upward at speed $v$ through a uniform magnetic field $\vec{B}$ to the right, with the rod perpendicular to both $\vec{v}$ and $\vec{B}$. Charges in the rod experience the magnetic force $q,\vec{v}\times\vec{B}$, separating charges and creating a motional EMF. For this geometry, $\mathcal{E}=BLv$, and if the rod is part of a closed circuit, a current flows. Lenz’s Law predicts a magnetic force on the rod opposing its motion. How does Lenz's Law apply to the situation described?