Rankers Physics

Motional EMF: Practice Problem & Solution

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 Explained:

To solve this problem, we apply the core principles of Motional EMF. Understanding the underlying formula is key to arriving at the correct answer below:

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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