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Rotating a Coil

  1. Mar 12, 2014 #1
    1. The problem statement, all variables and given/known data
    A rectangular coil of wire has 65.0 turns and is 30.0cm by 43.0cm . Initially the plane of the coil is perpendicular to a uniform external magnetic field. It is then rotated till its plane is at an angle of 35.0∘ with that field. The magntude of the external field is 1.90T and total time to rotate the coil is 7.00×10−2s .

    Calculate the magnitude of the average emf that is induced in the coil.

    2. Relevant equations

    Faraday's law

    3. The attempt at a solution

    So Faraday's law states that the induced emf is equal to [itex]\frac{-d\Phi_{B}}{dt}[/itex].
    What I get is
    A is area
    A = (0.3m)(0.43m) = 0.129m^2
    B is magnetic field
    dB/dt = (1.90T)/(7.00*10^2 s) = 27.14 T/s
    [itex]\frac{-d\Phi_{B}}{dt}[/itex] = -dB/dt * A * cos(35) = -2.87
    N is # of turns
    EMF = N * ([itex]\frac{-d\Phi_{B}}{dt}[/itex]) = 65 * -2.87 = -186

    This number seems very large to me. Can anyone point out what I've done wrong?
    Many thanks!
     
  2. jcsd
  3. Mar 13, 2014 #2

    rude man

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    Homework Helper
    Gold Member

    According to your formula, if the angle = 0 you get even more voltage! So we get big volts and we don't even move the coil! So that's bad.

    What is average emf? What is the average of a function f(t) over a time interval T?
    You need to integrate the emf and then divide by T. The emf varies how as you rotate the coil away from 0 degrees?

    I would initially replace the coil dimensions with a and b, the field with B, the final angle with θf and the no. of turns with N, then substitute actual numbers only at the very end. That way you can check dimensions of your terms and keep the math nice and tidy.
     
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