A wheel of radius 2 m having 8 conducting radial spokes is rotating about its geometrical axis with an angular velocity of 10 rad s⁻¹ in a uniform magnetic field of 0.2 T perpendicular to its plane. The induced emf between the rim of the wheel and its centre is V.

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(3) 4. Given: R = 2 m; ω = 10 rad s⁻¹; B = 0.2 T perpendicular to the wheel; 8 spokes. Idea: each spoke is a rod rotating about one end, so its emf is ε = 1/2Bω R² (the average speed along it is (ω R)/2). All 8 spokes join the hub to the rim, so they are in parallel: the emf between hub and rim is that of one spoke. ε = 1/2 × 0.2 × 10 × 2² = 4 V. So the emf between the rim and the centre is 4 V.

A wheel of radius 2 m having 8 conducting radial spokes is rotating about its geometrical axis with an angular velocity of 10 rad s⁻¹ in a uniform magnetic field of 0.2 T perpendicular to its plane. The induced emf between the rim of the wheel and its centre is ______ V.

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