Chapter 30, Problem 19P

You are working in a factory that produces long bars of copper with a square cross section. In one section of the production process, the bars must slide down a plane inclined at an angle θ = 21.0° to the horizontal. It has been found that the bars travel with too high a speed and become dented or bent when they arrive at the bottom of the plane and must be discarded. In order to prevent this waste, you devise a way to deliver the bars at the bottom of the plane at a lower speed. You replace the inclined plane with a pair of parallel metal rails, shown in Figure P30.19, separated by a distance ℓ = 2.00 m. The smooth bars of mass m = 1.00 kg will slide down the smooth rails, with the length of the bar always perpendicular to the rails. The rails are immersed in a magnetic field of magnitude B, and a resistor of resistance R = 1.00 Ω is connected between the upper ends of the rails. Determine the magnetic field necessary in your device so that the bars will arrive at the bottom of the plane with a maximum speed v = 1.00 m/s.

Figure P30.19 Problems 19 and 20.