Chapter 28, Problem 31P

You are in charge of planning a physics magic show for an open house on your campus. You come up with the following plan for one trick. You will place a sphere on a rough inclined plane of angle θ, as shown in Figure P28.31, and it will not roll down the incline. Here is the secret that only you know: The sphere is nonconducting, has a mass of 80.0 g, and a radius 20.0 cm. A flat, compact coil of wire with five turns is wrapped tightly around it, with each turn concentric with the sphere. The sphere is placed on the incline so that the coil is parallel to the plane. You establish a uniform magnetic field of 0.350 T vertically upward in the region of the sphere. (a) What current in the coil do you need to make this trick work? (b) You explain the trick to a friend in confidence and he suggests lowering the angle θ of the plane to make the required current lower. How do you respond?

Figure P28.31