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Magnetic Field with Time Dependence

  1. Feb 15, 2007 #1
    1. The problem statement, all variables and given/known data

    A magnetic field with the time dependence shown in the figure below is at right angles to a N=197 turn circular coil with a diameter of d=4.2 cm.


    What is the induced EMF in the coil at t=7.5ms in mV?

    See attached graph


    2. Relevant equations

    |EMF|= N*|change in magnetic flux/change in time|



    3. The attempt at a solution

    First Attempt:
    I first found Area by pi*(.042m/2)^2 and got 0.001385m^2. Then, I found the slope of the line between 5 and 10 ms, which was -0.006 T/ms. Then, I multiplied this slope by 7.5ms to see what the magnetic field at 7.5ms was, and I got -0.45T. Then, I used this value to find the magnetic flux which was (0.001385m^2)(-0.045T) and got -6.235*10^-5. Then, I took this value, divided by 7.5ms, and got -0.00831. Then, I multiplied this by 197 and got -1.63707 V. I divided this by 1000 and got -0.001637mV, but this answer is not being accepted.
     

    Attached Files:

  2. jcsd
  3. Feb 15, 2007 #2

    Doc Al

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    Staff: Mentor

    Good.
    All good, so far. And this is almost all you need.

    Hint: You've already calculated the rate of change of the field, so what's the rate of change of the flux?

    (The flux doesn't matter--only the rate of change of the flux.)
     
  4. Feb 15, 2007 #3
    To find the rate of change of the flux, I did:

    (B @ 10ms * Area) - (B @ 5ms * Area) all divided by (10ms-5ms)
    (-0.01T*0.001385)-(0.02T*0.001385)/(5ms) and got 4.155*10^-5 as the rate of change of the flux

    I then multiplied 4.155*10^-5 by 197, and got 0.008185, which I then divided by 1000, and got 8.18535mV, however, this is still not the right answer.

    Is my reasoning flawed or am I missing an essential step?
     
  5. Feb 15, 2007 #4

    Doc Al

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    Staff: Mentor

    Your reasoning is fine; check your arithmetic.
     
  6. Feb 15, 2007 #5
    Ok, let's try this step by step:

    I redid my arithmetic here, and as the rate of change of flux, I now got -0.00831

    Is this correct?

    Also, Thank you very much for your help!:smile:
     
  7. Feb 16, 2007 #6

    Doc Al

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    Staff: Mentor

    Looks good to me. (Units: T/s)
     
  8. Feb 16, 2007 #7
    Ok, now that I have the rate of change of flux, in order to find the induced EMF, in mV:

    I multiplied the rate of change of flux by the number of turns (197)

    (-0.00831 T/s)(197)= -1.63707 V

    then to get mV: -1.63707 V/1000 = -0.001637 mV

    Correct?


    If this is the correct way to do it, it is still the wrong answer when I enter it in my homework online :confused:
     
  9. Feb 16, 2007 #8

    I got it! I figured out what I was doing wrong. I had to divide by 10^-3, not 1000, and got 1637.07 mV, which was the right answer. Thanks for all your help!
     
  10. Feb 16, 2007 #9

    Doc Al

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    Staff: Mentor

    Check this step. (How many mV in a Volt? :wink: )

    (edit: Looks like you figured that out on your own!)
     
    Last edited: Feb 16, 2007
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