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A right-angled triangular loop abc made of metallic wire moves with uniform speed v in its own plane through a uniform magnetic field B that is directed perpendicular to the plane of the loop. The right angle is at b, with bc the side along the direction of motion. Find the EMF induced in the closed loop abc.

1. Zero
2. B v (bc)
3. B v (ac)
4. B v (ab)

Correct answer: Zero

Solution

The EMF around a closed loop equals -d(flux)/dt. In a uniform magnetic field perpendicular to the loop's plane, the flux is B times the loop area. As the rigid triangular loop translates with constant velocity in its own plane, its enclosed area does not change, so the flux is constant and d(flux)/dt = 0. Therefore the net EMF induced in the closed loop abc is zero (the motional EMFs of the individual segments cancel around the loop).

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