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Homework Help: Enduced emf in a loop

  1. May 16, 2013 #1
    1. The problem statement, all variables and given/known data
    A small loop with area 6.8 mm^2 is placed in a long solenoid with 854 turns/cm and a sinusoidally varying current w/ amplitude 1.28 A and angular frequency of 212 rad/s. What is the amplitude of the emf induced in the loop?

    2. Relevant equations
    [itex]\textbf{B}=\mu_0 in[/itex]
    [itex]\Phi_B = BA[/itex]
    [itex]emf = \frac{d\Phi_B}{dt}[/itex]

    3. The attempt at a solution
    Since the current is changing, the emf through the loop should be [itex]\mu_0 n A \frac{di}{dt}[/itex]
    If the angular frequency is 212 rad/s, then the current changes by 1.28 A in half a period, which is [itex]\frac{\pi}{212}[/itex] seconds. So the induced emf should be 6.29E-5 V, but the answer is .198 mV.
  2. jcsd
  3. May 16, 2013 #2

    rude man

    User Avatar
    Homework Helper
    Gold Member

    Does not make sense to me.

    If the current is i*sin(wt), what is di/dt? The rest of what you did looks OK.

    BTW I also get 0.198 mV.
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