NEET Physics Question - Electromagnetic Induction

A wheel with ten metallic spockes each 0.50 m long is rotated with a speed of 120 rev/min in a plane normal to the earth's magnetic field at the place. If the magnitude of the field is 0.4 Gauss, the induced e.m.f. between the axle and the rim of the wheel is equal to :

\[1.256\times 10^{-3} V\]

\[6.28\times 10^{-4} V\]

\[1.256\times 10^{-4} V\]

\[6.28\times 10^{-5} V\]

Solution:

Using the formula for induced e.m.f. in a rotating conductor:

e = \frac{1}{2} B \omega L^2 = \frac{1}{2} B (2\pi f) L^2

Substituting

e = \frac{1}{2} \times (0.4 \times 10^{-4}) \times (4\pi) \times (0.5)^2 = 6.28 \times 10^{-5}\text{ V}

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