3. (40 pts) A square loop of side a carrying a constant current Long SOIEI:)id I, is centered inside a long solenoid of radius s; > a and with n coils per meter. Assume that the wire making up the solenoid has zero resistance, but the ends of the solenoid Rotating loop wires are attached to a \"load\" (like a toaster :)) with (axis of . . . . rotation resistance R. The loop is rotating with constant angular \\ perpendicular frequency w on an axis perpendicular to the axis of the solenoid (and passing through the axis of the solenoid). Ignore any \"back EMF\" effects here (one can assume that the power source driving current [yadjusts such tht the current is always ;). a. (8 pts) A torque is required to keep the loop rotating Top view at constant w. Explain why. b. (12 pts) Find the torque 7 required to keep the loop rotating at angular frequency w. c. (12 pts) Show explicitly that w7, = I13,R/2, where I, is the amplitude of the current in the solenoid, and 7, 1s the time-averaged torque (i.e., averaged over one period of revolution). Argue based on general principles of power that this must be the case (hint, in mechanics, what does wt physically represent?) to page) d. (8 pts) A colleague of yours claims that as the load resistance decreases, approaching zero, the amount of power required to keep the loop turning also decreases and approaches zero. Is the correct? Justify your answer using a physical/physics explanation