JEE Main · 2024 · 30 Jan 2024 · Shift 1 · Electromagnetic Induction

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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

3 0^{\circ}

. The emf induced across the blades is

N π \times 1 0^{- 5}

V. The value of N is ______.

Answer: 32

Solution

Vertical component of Earth's field:

B_{V} = B sin 3 0^{\circ} = 0.5 \times 1 0^{- 4} \times \frac{1}{2} = 0.25 \times 1 0^{- 4} T

ω = 2 π (\frac{1200}{60}) = 40 π rad/s

.

EMF of a rotating blade of length

ℓ = 0.8 m

about one end:

ε = \frac{1}{2} B_{V} ω ℓ^{2} = \frac{1}{2} (0.25 \times 1 0^{- 4}) (40 π) (0.64) = 32 π \times 1 0^{- 5} V

.

So

N = 32

JEE Main · 2024 · 30 Jan 2024 · Shift 1 · Integer answer

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