11.1.13. A current flows through a conducting tape of width $d$. The tape is in a magnetic field of induction $B$. The field direction is perpendicular to its plane. Find the potential difference between points $1$ and $2$ of the tape if its thickness is $h$ and the bulk charge density of current carriers on it is $\rho$.
Solution
For problem $11.1.13$
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 $V=Ed=IB/(\rho h)$.
