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Math Help - Electromagnetic induction

  1. #1
    Newbie Siva's Avatar
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    Question Electromagnetic induction

    Can anyone help me derive an expression for the e.m.f induced in a coil rotating in a uniform magnetic field.

    let
    w= angular velocity etc..........
    Last edited by Siva; May 12th 2008 at 08:06 AM. Reason: srry my bad
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  2. #2
    Super Member Aryth's Avatar
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    When the coil is rotated at a uniform rate in a uniform horizontal magnetic field of intensity \vec{B}, then the induced e.m.f produced is given by:

    e = -\frac{d\phi}{dt}

    = -\frac{d}{dt}[N\vec{B}\cdot \hat{n} A]

    Where N = number of turns in coil

    and A = Area of coil

    = -\frac{d}{dt}[NBcos{\theta}A]

    = -NAB\frac{d}{dt}[cos{\theta}]

    = -NAB\left[-sin{\theta}\frac{d\theta}{dt}\right]

    = NAB\omega sin{\omega t}

    Where \omega = \frac{d\theta}{dt} = \frac{\theta}{t}, \text{as it is uniform}

    \therefore \ e = (NAB\omega)sin(\omega t)

    e = e_0 \ sin{(\omega t)}

    And there you go.
    Last edited by Aryth; May 17th 2008 at 06:02 PM.
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