A 30 N resistor is connected using stiff wires of negligible resistance to a 12 V ideal battery. The circuit is bent into a rectangle that is 0.20 m wide and very tall. The loop is then oriented vertically, so that the 0.20 m sides are horizontal and the long sides are vertical, and allowed to drop from a region with no magnetic field into a region of uniform magnetic field that points perpendicular to the plane of the circuit. The situation is shown below, with the field pointing out of the page indicated by the dots. (The battery and resistor are not shown.) Note that only the lower part of the loop is in the field; the top edge is in the region where the field is zero. (a) If we want the force by the field to slow the loop's fall, in what direction should the current flow (using the view shown in the diagram)? (b) If the whole circuit has mass m=0.010 kg, what magnetic field do we need in order for the upward magnetic force is equal to the loop's weight (ie no net force)? Assume the loop is tall enough that the top doesn't reach the region with field.

A 30 N resistor is connected using stiff wires of negligible resistance to a 12 V ideal battery. The circuit is bent into a rectangle that is 0.20 m wide and very tall. The loop is then oriented vertically, so that the 0.20 m sides are horizontal and the long sides are vertical, and allowed to drop from a region with no magnetic field into a region of uniform magnetic field that points perpendicular to the plane of the circuit. The situation is shown below, with the field pointing out of the page indicated by the dots. (The battery and resistor are not shown.) Note that only the lower part of the loop is in the field; the top edge is in the region where the field is zero. (a) If we want the force by the field to slow the loop's fall, in what direction should the current flow (using the view shown in the diagram)? (b) If the whole circuit has mass m=0.010 kg, what magnetic field do we need in order for the upward magnetic force is equal to the loop's weight (ie no net force)? Assume the loop is tall enough that the top doesn't reach the region with field.