Chapter 30, Problem 44AP

A conducting rod of length ℓ moves with velocity $\stackrel{\to }{v}$ parallel to a long wire carrying a steady current I. The axis of the rod is maintained perpendicular to the wire with the near end a distance r away (Fig. P30.44). Show that the magnitude of the emf induced in the rod is

$\left|\mathcal{E}\right|=\frac{{\mu }_{0}Iv}{2\pi }\ln \left(1+\frac{\mathcal{l}}{r}\right)$

Figure P30.44