A cylindrical conducting rod is kept with its axis along positive z-axis, where a uniform magnetic field exists parallel to z-axis. The current induced in the cylinder is

The induced emf $e$ in a conducting rod of length $l$, moving with a velocity $v$, in a uniform magnetic field, is given by,

              $e=Bvl\sin \theta$,

where $\theta =$ angle between $\vec{v}$ and $\vec{B}$,

in the given problem, as the rod is static i.e. $v=0$ and parallel to the magnetic field $\theta =0$ therefore induced emf in rod will be,               $e=0$,

hence,  $i=0$ (induced current)