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A conducting rod of length $L$ rotates with angular velocity $\omega$ about one end in a uniform magnetic field $B$ perpendicular to the plane of rotation. The induced emf between the ends is?
- A.$B \omega L^2$
- B.$0.5 B \omega L^2$
- C.$0.25 B \omega L^2$
- D.$2 B \omega L^2$
Show correct answer & step-by-step solution
Correct answer: B — $0.5 B \omega L^2$
Solution
The emf induced in a small element at distance is . Integrating this from to yields the total emf as .
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