Answer
See answers.
Work Step by Step
a. See in Figure 21–11a . The induced current is clockwise, to make more magnetic field lines into the page, fighting the increasing number of B field lines pointing out of the page as the rod slides through the field.
So, the current flowing in the rod is from top to bottom. The amount is the induced emf ($\epsilon = B\mathcal{l}v$) divided by the resistance. The flowing current is in a magnetic field, and by the right-hand rule, the bar feels a magnetic force to the left, $I\mathcal{l}B$. The external force to the right is equal and opposite since the rod moves at constant speed.
$$F_{external}=F_{mag}=I\mathcal{l}B=\frac{\epsilon}{R}\mathcal{l}B=\frac{B\mathcal{l}v}{R}\mathcal{l}B=\frac{B^2\mathcal{l}^2v}{R} $$
b. The power required is the external force multiplied by the speed of the rod.
$$P=F_{external}v=\frac{B^2\mathcal{l}^2v^2}{R} $$
