A wheel with 10 metallic spokes, each 0.5 m long, is rotated with a speed of 120 rev min⁻¹ in a plane normal to the horizontal component of the earth's magnetic field B_H at a place. If B_H = 0.4 G at the place, what is the induced emf between the axle and the rim of the wheel? (1 G = 10⁻⁴ T)

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(4) 62.8 μV. Given: spoke length ℓ = 0.5 m, B_H = 0.4 G = 0.4×10⁻⁴ T, speed 120 rev min⁻¹ = 2 rev s⁻¹. Angular speed: ω = 2π×2 = 4π rad s⁻¹. Idea: a rod of length ℓ rotating about one end in a plane perpendicular to B develops ε = 1/2Bωℓ² between its ends. ε = 1/2×(0.4×10⁻⁴)×4π×(0.5)² = 2π×10⁻⁵ ≈ 6.28×10⁻⁵ V. All ten spokes connect the same axle to the same rim with equal emfs, so they are in parallel: the number of spokes does not change the emf. Emf between axle and rim = 62.8 μV.

A wheel with 10 metallic spokes, each 0.5 m long, is rotated with a speed of 120 rev min⁻¹ in a plane normal to the horizontal component of the earth's magnetic field B_H at a place. If B_H = 0.4 G at the place, what is the induced emf between the axle and the rim of the wheel? (1 G = 10⁻⁴ T)

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