A straight conducting rod of length L is rotated at a constant angular speed ω in a plane perpendicular to a uniform magnetic field B about an axis passing through one of its ends. What is the electromotive force (EMF) induced between the two ends of the rod?

Answer and explanation

Correct answer: D. (1/2) B ω * L²

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  1. Step 1: Consider a small element of the rod at a radial distance from the axis of rotation.
  2. Step 2: The linear speed of this element is .
  3. Step 3: The motional EMF induced across this infinitesimal segment moving perpendicular to the magnetic field is:
  4. Step 4: Integrate from to :
Answer
(1/2) B ω * L²
Why not the others: 'B ω L²' uses the tip speed over the entire rod length instead of integrating the linear velocity gradient; '2 B ω L²' multiplies by 2 instead of dividing by 2; '(1/4) B ω L²' incorrectly divides by 4.

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