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Electromagnetic Induction Question

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    How do the formulae,

    induced emf = (-) rate of change of magnetic flux linkage


    induced emf = BANwsin(wt)

    corroborate each other?

    I.e. let's say a coil rotates 90 degrees. Hence, the change in induced emf would be its maximum value. According to the second equation, this would be BANw.

    Hence, from the second equation, induced emf = BANw = BAN(2pie)/T

    However, when looking at the first equation: through the 90 degree rotation, the change in magnetic flux linkage would also equal its maximum value, which is BAN.

    Hence, from first equation, induced emf = BAN/T

    Therefore the two equations do not lead to the same result???

    I think I have answer to the question. They will lead to the same result. You aren't looking at it right. Farradays law states that the induced emf is the Rate of change of flux linkage. Your equation doesn't show that. You said emf = BAN / T which is wrong. Emf = N ΔΦ /ΔT (where ΔΦ is the change of flux BA).

    Some more insight. The flux linkage will change continously in a rotating coil. So NΦ = BAN cos(2π ft) where 2π ft = angle.
    The diffrential of this with respect to time gives :

    N ΔΦ /ΔT = (-)BAN(2π f) sin(2π ft)

    This is your second equation. The gradient of a graph with flux lnikage of rotating coil against time is the emf. So they will give the same value. You are reading it wrong that's all. I hope that helps.
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