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A straight wire of length 2 m is held perpendicular to the xy-plane and moved with velocity v = (2i + 3j + k) m/s through a region of magnetic field B = (i + 2j) Wb/m². Find the potential difference induced between the ends of the wire.

1. 2 volts
2. 4 volts
3. 0 volts
4. none of these

Correct answer: 2 volts

Solution

The wire is perpendicular to the xy-plane, so its length vector is L = 2k. The motional emf = (v x B).L. Compute v x B with v = (2,3,1) and B = (1,2,0): v x B = (3*0 - 1*2, 1*1 - 2*0, 2*2 - 3*1) = (-2, 1, 1). Dot with L = (0,0,2): emf = 1*2 = 2 V. Magnitude 2 volts.

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