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Induced Emf

  1. Mar 30, 2006 #1
    A magnetic field with the time dependence shown in Figure 23-38 is at right angles to a 181 turn circular coil with a diameter of 3.91 cm. What is the induced emf in the coil at each of the following times?

    [​IMG]

    (a) t = 2.50 ms
    0 V
    (b) t = 7.50 ms

    (c) t = 15.0 ms
    0 V
    (d) t = 25.0 ms

    N = 181
    A = .01955[tex]^2[/tex]

    i've gotten (a) and (c) right but am having a very hard time with (b) and (d). for (b) i've been doing [tex]\phi[/tex] = BA cos [tex]\theta[/tex] where [tex]\theta[/tex] = 0 for t= 7.50 m/s as the final flux and then at t= 2.50 m/s for the initial flux . Then to find induced emf i've been doing 181(([tex]\phi_{f}[/tex] - [tex]\phi_{i}[/tex])/(7.50 - 2.50)) but am getting the wrong answer, what am i doing wrong??
     
    Last edited: Mar 30, 2006
  2. jcsd
  3. Mar 30, 2006 #2
    can anyone help me?
     
  4. Mar 30, 2006 #3

    nrqed

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    To be honest, I am really not following what you did.

    But the induced emf is (dropping all signs) N A cos (theta) dB/dt in your case (only the magnitude of B changes). And dB/dt is simply the slope of the graph. So for the emf at 7.50 ms, the slope of the graph is dB/dt = (-0.01 - 0.02)/(10 ms - 5 ms) . Dropping the sign, multiplying by N A should give you the answer.


    Patrick
     
  5. Mar 30, 2006 #4
    (-.01-.02)/(10-5) = -.006

    dropping the sign: (181) (.006) [tex]\pi[/tex] (.01955[tex]^2[/tex])

    i get .001303 V but thats not right :confused:

    edit: fixed
     
    Last edited: Mar 30, 2006
  6. Mar 30, 2006 #5

    nrqed

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    You seem tohave forgotten to multiply r^2 by Pi !
     
  7. Mar 30, 2006 #6
    oops sorry that was supposed to have [tex]\pi[/tex] in there, i didn't forget it in my calculation
     
  8. Mar 30, 2006 #7

    nrqed

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    You must put dB/dt in Tesla per second...so it`s 6 Tesla/second
     
  9. Mar 30, 2006 #8
    ooooooohhhh ok, but why isn't it already in T/s??
     
  10. Mar 30, 2006 #9

    nrqed

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    Because the time you divided by was in milliseconds.
    Do you get the right answer now? I need to go to bed :wink:
     
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