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A magnetic field points into the plane of the page. A rod of length l moves in this field so that its bottom end has velocity v1 and its top end has velocity v2 (with v2 > v1). The emf induced across the rod is:

1. B*v1*l
2. B*v2*l
3. (1/2)*B*(v2 + v1)*l
4. (1/2)*B*(v2 - v1)*l

Correct answer: (1/2)*B*(v2 + v1)*l

Solution

Since the rod's velocity varies linearly from v1 (bottom) to v2 (top), the average velocity is (v1 + v2)/2. Motional emf = B * (average velocity) * l = (1/2)*B*(v1 + v2)*l.

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