AP Free Response Question 2001 C3 E&M
The circuit shown below consists of a battery of emf  in series with a rod of length L, mass m, and resistance R. The rod is suspended by vertical connecting wires of length d, and the horizontal wires that connect to the battery are fixed. All these wires have negligible mass and resistance. The rod is a distance r above a conducting cable. The cable is very long and is located directly below and parallel to the rod. Earth's gravitational pull is toward the bottom of the page.

Express all algebraic answers in terms of the given quantities and fundamental constants.

 a. What is the magnitude and direction of the current I in the rod?

 b. In which direction must there be a current in the cable to exert an upward force on the rod? Justify your answer.

 c. With the proper current in the cable, the rod can be lifted up such that there is no tension in the connecting wires. Determine the minimum current Ic in the cable that satisfies this situation.

 d. Determine the magnitude of the magnetic flux through the circuit due to the minimum current Ic determined in part c.