Solution

Consider a section of the tape of length $l$. The magnetic force on the charge in the tape is $F=IlB$. In this section of the tape, the total charge is $Q=\rho dlh$. Consequently, the force per unit charge $F/Q=IB/(\rho dh)$ is equivalent to an electric field $E$. Thus, the potential difference between the near edge and the far edge of the tape is $V=Ed=IB/(\rho h)$.