Question

An insulating sphere of mass M and radius R is wrapped with N coils of wire around its equator. The sphere is placed on an incline at an angle θ in a uniform magnetic field of strength B. The goal is to keep the sphere from rolling down the incline by having a current in the coils. [Recall, the force of static friction at the point of contact creates a torque about the center of the sphere, which is what causes the sphere to rotate in a way that rolls it downhill.] θ B~ (a) [3 pts.] To keep the sphere in place, must the current in the coils circulate clockwise or counter-clockwise as seen from above? Explain. (b) [6 pts.] Determine an expression for the current, Io, that is needed to keep the sphere in place. (c) [2 pts. each] Assume that the magnitude of current needed to keep the sphere balanced is Io. For each of the following changes to the system, explain whether Io would have a larger value, a smaller value, or the same value. Explain your answers based on physical reasoning—your expression from part (b) should support your answer, but does not explain it. Consider each change individually (i.e., the change made in one part is not present in the other parts). i. The mass of the sphere increases (but the radius stays the same). ii. The radius of the sphere increases (but the mass stays the same). iii. The number of coils increases. iv. The strength of the magnetic field increases. v. The angle of the incline increases (but remains less than 90◦ ).

Answer 1