JEE MAIN - Physics (2024 - 30th January Morning Shift - No. 30)
A ceiling fan having 3 blades of length $$80 \mathrm{~cm}$$ each is rotating with an angular velocity of 1200 $$\mathrm{rpm}$$. The magnetic field of earth in that region is $$0.5 \mathrm{G}$$ and angle of dip is $$30^{\circ}$$. The emf induced across the blades is $$\mathrm{N} \pi \times 10^{-5} \mathrm{~V}$$. The value of $$\mathrm{N}$$ is _________.
Answer
32
Explanation
$$\begin{aligned}
& B_v=B \sin 30=\frac{1}{4} \times 10^{-4} \\
& \omega=2 \pi \times f=\frac{2 \pi}{60} \times 1200 \mathrm{~rad} / \mathrm{s} \\
& \varepsilon=\frac{1}{2} B_V \omega \ell^2 \\
& =32 \pi \times 10^{-5} \mathrm{~V}
\end{aligned}$$
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