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Homework Help: Induced emf at a specific time

  1. Oct 28, 2009 #1
    1. The problem statement, all variables and given/known data

    A circular coil with 35 turns of wire and a diameter of 19 cm is placed in a magnetic field given by B(t) = 6 t^2 + 6 t + 2 T where t is time in seconds. The field is perpendicular to the plane of the coil. What is the induced EMF at t = 5 s?

    2. Relevant equations

    E=-d(magnetic flux)/dtime

    3. The attempt at a solution
    I found E to be 36.12 V but that's wrong. I'm not sure what's wrong. I did E=NAB/time.
    Last edited: Oct 28, 2009
  2. jcsd
  3. Oct 28, 2009 #2
    Emf is proportional to negative the derivative or rate of change of the magnetic flux with respect to time. The area is constant, thus
    V = -NA*dB/dt.
  4. Oct 28, 2009 #3
    I plugged in -36.12 but it's still wrong. Can we have a negative voltage?
  5. Oct 28, 2009 #4
    Could you please tell me where I'm wrong? I have a couple of hours left.
  6. Oct 28, 2009 #5
    dB/dt = 12t + 6; at t = 5s, dB/dt = 66T/s
    N = 35 turns
    A = pi*r^2...so your problem might be that you're using the diameter of 19cm instead of the radius; also, be sure that you convert the given units to the proper units, so the radius = d/2 = 9.5cm = .095m.
    The emf is V = -NA*dB/dt....and you could have a negative voltage.
  7. Oct 28, 2009 #6
    Thank you very much I appreciate it.
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