The situations below show eight rectangular wire loops that are moving to the ri

Question

The situations below show eight rectangular wire loops that are moving to the right into, within or out of, a region in which there is uniform magnetic field coming out of the page. The rectangular loops are the same size (5 cm by 10 cm) and are being pushed to the right at a constant velocity (2 cm/s). The loops are at various locations with various portions (25%, 50%, 75%, or 100%) within the field and orientations in the field as shown. Rank these situations, from greatest to least, on the basis of the magnitude of the current in the rectangular loops at the time and positions shown (assume there is no effect or interaction between the loops). Greatest OR, All the loops have the same current. _____ OR, There is no current in any of the loops. _______ Carefully explain your reasoning.

Explanation / Answer

Greatest 1 F 2 A_ 3 C 4 G 5 B 6 D 7 E 8 H Least

The current is directly proportional to the induced emf since they all have same resistance due to same circumference. The induced emf is proportional to the rate of change of flux. BDEH has no change in flux since the portion within the magnetic field is constant (until they reach the limit of the field). For the others, the rate of change of flux is due to change of area that is proportional to the length of the rectangle perpendicular to the direction of motion. (Or, Emf = BvL where L is the length perpendicular to direction of motion and since B and v are constant the emf is proportional to L.)

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