A square, conducting wire loop of side L, total mass m. and total resistance R initially lies in 1he horizontal xy-plane, with corners at (x, y, z) = (0,0,0), (0,L,0), (L, 0, 0), and (L.L.O). There is a uniform upward magnetic field B = Bk in the space wi1hin and around 1he loop. The side of 1he loop 1hat extends from (0, 0, 0) to (L, 0, 0) is held in place on the x-axis; the rest of the loop is free to pivot around this axis. When 1he loop is released, it begins to rotate due to 1he gravitational torque. 

(a) Find 1he net torque (magnitude and direction) that acts on the loop when it has rotated 1hrough an angle '" from its original orientation and is rotating downward at an angular speed cu. 

(b) Find the angular acceleration of 1he loop at the instant described in part (a).

(c) Compared to the case with zero magnetic field does it take 1he loop a longer or shorter time to rotate 1hrough 900? Explain. 

(d) Is mechanical energy conserved as the loop rotates downward? Explain.