A metallic conductor of length 1 m rotates in a vertical plane parallel to east-west direction about one of its end with angular velocity 5 rad s ⁻¹. If the horizontal component of earth's magnetic field is 0.2 × 10 - 4 T, then emf induced between the two ends of the conductor is: (a) 5 μ V (b) 50 μ V (c) 5 mV (d) 50 mv

Answer: (b). Plane of rotation is vertical E-W, so the horizontal (northward) component BH is normal to it. e = 1/2BHω l² = 1/2 × 0.2 × 10⁻⁴ × 5 × 1² = 5 × 10⁻⁵ V So the answer is (b) 50 μ V.

A metallic conductor of length 1 m rotates in a vertical plane… | JEE Main 2022 (26 Jun, Shift 2)

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Rotating Conductors & AC Generator

A metallic conductor of length 1 m rotates in a vertical plane parallel to east-west direction about one of its end with angular velocity 5 rad s ${}^{-1}$ . If the horizontal component of earth's magnetic field is 0.2 $\times$ 10 $-$ 4 T, then emf induced between the two ends of the conductor is:

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Answer: (b)

Plane of rotation is vertical E-W, so the horizontal (northward) component $B_H$ is normal to it.
$e = \tfrac{1}{2}B_H\omega l^2 = \tfrac{1}{2} \times 0.2 \times 10^{-4} \times 5 \times 1^2 = 5 \times 10^{-5}\text{ V}$
So the answer is (b) 50 $\mu$ V.

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