Consider the arrangement shown in Figure. A conductor bar of length l is free to move along a pair of conducting rails. The bar is driven by an external force at a constant velocity of U m/s. A constant uniform magnetic field ¯B is present, pointing into the paper of the book page.

Neglect the resistance of the bar and rails, as well as the friction between the bar and the rails.

(a) Determine the expression for the motional voltage across terminals 1 and 2. Is terminal 1 positive with respect to terminal 2?

(b) If an electric load resistance R is connected across the terminals, what are the current and power dissipated in the load resistance? Show the direction of current on the figure.

(c) Find the magnetic-field force exerted on the moving bar, and the mechanical power required to move the bar. How is the principle of energy conservation satisfied?

(d) Since the moving bar is not accelerating, the net force on the bar must be equal to zero. How can you justify this?