Voltage across rod in time varying magnetic field

If a slim conductor of some length $l$ and diameter $dll l$ is placed in a magnetic field $B$, and the field is changed by $frac {dB}{dt}$, what (if any) is the voltage $V$ induced across the ends of the conductor?

In my case of interest, the slim conductor is a wire, fixed in space, that is victim of interference by an adjacent current, where the $frac {dB}{dt}$ is caused by $I sin(omega t)$ in a source wire.

I am particularly interested in calculating a specific case (given $I_0$, $omega$, and $r$ the distance between the two wires), as well as the fundamental connections to Maxwell’s laws, probably the Maxwell- Faraday equation.

I am familiar with Lenz’s law , but in my case of interest there is no return path or "ground plane", and so the victim wire has no current loop, or EMF loop. I can’t form a curl integral, and no area is determined, and thus no time varying flux. Nevertheless, I would expect the above "wire rod" case to be the Maxwellian foundation of, or at least a step towards the Lenz "loop around flux" case. (Or perhaps I am terribly on the wrong foot here.)

The closest I come to this problem is by the Lorentz force , as it also involves a rod, and it involves a EMF on a charge in motion in a magnetic field. In contrast, my question centers around a time-varying magnetic field, without motion.

To be clear, the rod is fixed in space, and I am interested in the voltage calculation, not the motion or forces.

(Image from https://www.aplusphysics.com/courses/regents/electricity/images/InductionProblem.png)