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Homework Help: Faraday Law problem

  1. Jan 8, 2009 #1
    1. The problem statement, all variables and given/known data

    A long solenoid of radius a , is driven by an alternating current , so that the field inside is sinusoidal: B(t)=B0cos(omega*t)z-hat. A circular loop of wire, of raduis a/2 and resistance R, is placed inside the solenoid and coaxial with it. Find the current induced in the loop , as a function of time.

    2. Relevant equations

    I=[tex]\epsilon[/tex]/R
    [tex]\Phi[/tex]=[tex]\int[/tex]B[tex]\cdot[/tex] da

    [tex]\epsilon[/tex]=[tex]\int[/tex]E[tex]\cdot[/tex]dl=[tex]\int[/tex](dB/dt)[tex]\cdot[/tex]da

    3. The attempt at a solution

    dB/dt=-omega*B0sin(omega*t)z-hat
    [tex]\epsilon[/tex]=[tex]\int[/tex]omega*B0sin(omega*t) da, since the area of a circle is pi*r2, da is just pi*r2

    I=omega*B0*sin(omega*t)*[tex]\pi[/tex]a2/(R)

    episilon is supposed to be the electromotive force BTW.
     
  2. jcsd
  3. Jan 9, 2009 #2
    Excuse me, but I think among 'da=pi*r^2', r should be a/2
     
  4. Jan 9, 2009 #3
    What about my remaining solutions?
     
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