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