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Homework Help: Maximum Induced Emf

  1. Nov 27, 2009 #1
    1. The problem statement, all variables and given/known data

    A flat loop of wire of area 15.7 cm2 and 1.09 turns is perpendicular to a magnetic field whose magnitude decays in time according to B = 0.5 e−t/7. What is the maximum induced emf? Answer in units of V.

    2. Relevant equations

    [tex]\epsilon=[/tex] [tex]\Delta[/tex][tex]\Phi[/tex]B/[tex]\Delta[/tex]t

    [tex]\epsilon=[/tex] - (dB/dt) N A Cos[tex]\theta[/tex]

    3. The attempt at a solution

    I have:

    A = 15.7 X 10-4 m2

    N = 1.09 turns

    B = 0.5 e-t/7

    Maximum [tex]\epsilon[/tex] = E max. = ??

    I found E max. = - ( 1.09) * ( 15.7 X 10-4 ) * Cos(0) * d(0.5 e-t/7)/dt

    = 1.22 X 10-4 e-t/7

    Then i found the first deravative of induced emf in terms of time & got another equation.
    Then i made that equation equal to zero to find value of time for max. [tex]\epsilon[/tex].
    But there is no such value for time. Calculator says false everytime which is true.

    I tried to take the second deravative and equalize to zero and again same paroblem occured.

    Soooo any help will be appreciated.
  2. jcsd
  3. Nov 27, 2009 #2


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    So what is the maximum value of E? More to the point, at what time is the above expression a maximum and what is that maximum value?
    Last edited: Nov 27, 2009
  4. Nov 27, 2009 #3
    Wow , thx kuruman for the help , it is right , when time is zero i get a maximum emf E.

    but i have a question ,,, can i find the maximum by deravatives and how and when to use ???

    thx in advance for all who are helping us ... ^^
  5. Nov 27, 2009 #4


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    You cannot find the maximum by derivatives because the exponential function does not a maximum or minimum. It is either monotonically decreasing or increasing.
  6. Nov 28, 2009 #5
    thanks kuruman for eplanation. I understood now why i couldn't find a maximum value when deriving the equation. thanks a lot man .
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