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Rotating coil in a model ac generator. Finding smallest value of time for maximum emf

  1. Oct 16, 2012 #1
    1. The problem statement, all variables and given/known data
    In a model ac generator, a 500 turn rectangular coil, 8.0 cm by 20 cm, rotates at 120 rev/min in a uniform magnetic field of 0.60 T.

    (a) What is the maximum emf induced in the coil?
    (b) What is the instantaneous value of the emf in the coil at t = (∏/32)s? Assume that the emf is zero at t = 0.
    (c) What is the smallest value of t for which the emf will have its maximum value?

    2. Relevant equations
    εmax=NBAω
    ε=εmaxsinωt

    3. The attempt at a solution
    I easily understand part a and b (below):
    (a)
    Area=0.08x0.20=0.016 m2
    120rev/min = 12.56 rad/s

    εmax=NBAω
    εmax=500(0.60)(0.016)ω
    εmax=60.28V

    (b)
    ε=εmaxsinωt
    ε=60.28sin(12.56∏/32)
    ε=56.87V

    (c)
    Part c is where I am totally confused. We did this problem in class, so I will show you what my teacher came up with and explain why I don't understand.

    ε=εmaxsinωt
    ωt=∏/2 --> ε=εmax
    12.56t=∏/2
    t=∏/2(12.56)=0.125 s

    I do not understand where/how my teacher came up with ωt=∏/2. Why are we dividing pi by 2? And how do we know this is equal to ωt? Are we just supposed to know this equation? Is it a common physics rule? I want to know the "why" behind it and not just memorize that equation so I can apply it to other situations. For instance, what if we're asked what the largest value of t for which the emf will have it's maximum value?" Then it wouldn't still be pi over 2?

    I have a test Thursday and have been wracking my brain trying to figure out why or how he came up with part c. I would greatly appreciate any and all help. Thank you so much!!!! :!!)
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 17, 2012 #2

    tiny-tim

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    welcome to pf!

    hi mydoghenry! :smile:
    the maximum value of sin (= 1) is when the angle is π/2 :wink:
     
  4. Oct 17, 2012 #3
    Re: Rotating coil in a model ac generator. Finding smallest value of time for maximum

    Thank you so very, very much. It makes sense now. I must have missed the day in class when we learned ∏/2 is the radian form of 90°.

    Do you think there's any other way for that question to be asked? For instance, What is the smallest value of t for which the emf will have its minimum value? In this case would it be sin180 (aka sin∏) which I guess is zero. So, maybe there's only one way he'd ask this question.
     
  5. Oct 17, 2012 #4

    tiny-tim

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    yes …

    he's really not trying to trick you! :smile:
     
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