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A straight conducting rod moves with constant velocity v perpendicular to a long straight wire carrying current I, the rod lying in the plane of the wire at distance r (as shown). Find the magnitude of the emf induced between the ends of the rod (rod length and geometry per the figure giving a simple inverse-r dependence).

1. mu0 v I / (pi r)
2. mu0 v I / (2 pi r)
3. 2 mu0 v I / (pi r)
4. mu0 v I / (4 pi r)

Correct answer: mu0 v I / (2 pi r)

Solution

The magnetic field of the long wire at the rod is B = mu0 I/(2 pi r). The motional emf is the line integral of (v x B) along the rod, which for the shown geometry gives emf = B v (per unit length factor absorbed) = mu0 v I/(2 pi r).

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