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The induced electromotive force is given by e = -M (di/dt) = -0.005 × (di₀ sin ωt/dt). Which of the following statements is correct?

1. The induced emf is -0.005 × i₀ × (cos ωt).
2. The maximum emf is 0.005 × i₀ × ω when cos ωt equals -1.
3. The value of emf is 0.005 × 10 × 100π = 5π volts.
4. If the conductor length is 0.4 m, moving at 7 m/s in a magnetic field of 0.9 Wb/m², the emf is induced.

Correct answer: The maximum emf is 0.005 × i₀ × ω when cos ωt equals -1.

Solution

The given equation represents the induced EMF, and the maximum EMF occurs when the derivative of the sine function is at its maximum, which is when cos(ωt) = -1. Substituting this condition gives eₘₐₓ = 0.005 × i₀ × ω.

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