= Solution
Use the coordinates in <8>. At downhill speed $v$, the moving bar has $\mathbf v\times\mathbf B=-Bv\cos\phi\,\hat{\mathbf b}$. The <electromotive force> and induced <electric current> are therefore
$$
\boxed{\mathcal E=Bs v\cos\phi,\qquad I=\frac{Bs v\cos\phi}{R}.}
$$
Here $I$ is positive along $-\hat{\mathbf b}$ across the sliding bar, then returns through the rails and <resistor>. This direction makes the <magnetic force> oppose downhill motion, as required by <Lenz's law>. The factor $\cos\phi$ is essential: only the component of <magnetic field> normal to the rail plane threads the circuit. Rail and bar <electrical resistances> and circuit <self-inductance> are neglected relative to the stated large $R$ model.
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