 Solution

The bar's motion increases positive $z$-directed magnetic flux at rate $B\ell v$. By Lenz's law, induced current circulates clockwise as viewed from positive $z$, producing a field into the page. Equivalently $\mathbf{v}\times \mathbf{B}=-vB\hat{\mathbf{y}}$ drives positive charge down the moving bar. The motional electromotive force has magnitude $B\ell v$, soThe current flows downward in the bar, left along the lower rail, upward through the resistor, and right along the upper rail. The ideal circuit approximation neglects self-inductance and the bar's resistance.