A ceiling fan having 3 blades of length 80 cm each is rotating with an angular velocity of 1200 rpm. The magnetic field of earth in that region is 0.5 G and angle of dip is 30°. The emf induced across the blades is Nπ × 10⁻⁵ V. The value of N is _________. Numerical answer type. Work it out, then open the answer.

Answer: 32. A ceiling fan rotates in a horizontal plane, so only the vertical component acts: BV = Bsin 30° = 0.25×10⁻⁴ T. ω = 1200 rpm = 20 rev/s = 40π rad/s Emf between centre and tip: e = 1/2BVω l² = 1/2 × 0.25×10⁻⁴ × 40π × 0.64 e = 3.2π×10⁻⁴ = 32π×10⁻⁵ V, so N = 32

A ceiling fan having 3 blades of length 80 cm each is rotating with… | JEE Main 2024 (30 Jan, Shift 1)

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Rotating Conductors & AC Generator

A ceiling fan having 3 blades of length $80\text{ cm}$ each is rotating with an angular velocity of 1200 $\text{rpm}$ . The magnetic field of earth in that region is $0.5\text{ G}$ and angle of dip is $30^\circ$ . The emf induced across the blades is $N\pi \times 10^{-5}\text{ V}$ . The value of $N$ is _________.

Numerical answer type. Work it out, then open the answer.

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Answer: 32

A ceiling fan rotates in a horizontal plane, so only the vertical component acts: $B_V = B\sin 30^\circ = 0.25\times10^{-4}\text{ T}$ .
$\omega = 1200\text{ rpm} = 20\text{ rev/s} = 40\pi$ rad/s
Emf between centre and tip: $e = \frac{1}{2}B_V\omega l^2 = \frac{1}{2} \times 0.25\times10^{-4} \times 40\pi \times 0.64$
$e = 3.2\pi\times10^{-4} = 32\pi\times10^{-5}\text{ V}$ , so $N = 32$

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