A wheel with 20 metallic spokes, each 1 m long, rotates at 120 rpm in a uniform magnetic field 0.4 G normal to its plane. Calculate emf between axle and rim. Take 1 G = 10⁻⁴ T.
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A wheel with 20 metallic spokes, each 1 m long, rotates at 120 rpm in a uniform magnetic field 0.4 G normal to its plane. Calculate emf between axle and rim. Take 1 G = 10⁻⁴ T.

G1 Physics · Accepted Answer

Step 1: A rotating spoke of radius R sweeps magnetic flux and acquires motional emf dε=Bωr dr. Step 2: Integrate from axle to rim: ε=∫(0→R) Bωr dr=(1/2)BωR². Step 3: Given B=0.4 gauss=0.4×10⁻⁴T, R=1m and 120rpm⇒ω=(120/60)×2π=4πrad/s. Step 4: ε=(1/2)(0.4×10⁻⁴)(4π)(1)²=0.8π×10⁻⁴V=2.51×10⁻⁴V. Answer A. Final answer: (A) 2.51 × 10⁻⁴ V.