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Constant angular speed loop of wire

  1. May 21, 2014 #1
    1. The problem statement, all variables and given/known data

    You have a loop of wire (dimensions c and d) which is oriented vertically on the y axis (the y axis splits the rectangle in two equal pieces), and rotates about the y axis at constant angular ##\omega##. The magnetic field is in the +i direction.

    What would be the torqque needed to have the loop rotate at a constant w?


    2. Relevant equations


    ##\tau = NIAB\sin\theta##


    3. The attempt at a solution

    ##\mathcal{E} = B(cd)\omega \sin( \omega t )## from Faraday's law.

    ##I = \dfrac{B(cd)\omega\sin (\omega t)}{R}##

    I am not sure how to proceed from here...what do I set the torque, ##\tau = NIAB\sin\theta## equal to?
     
    Last edited: May 21, 2014
  2. jcsd
  3. May 21, 2014 #2

    mfb

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    You have a current flow in a magnetic field. Do you see any forces from this?
     
  4. May 21, 2014 #3
    I see ##F_B = ILB\sin\theta##, however, I can't tell which direction they are going in, and doesn't it change as the loop rotates?
     
  5. May 21, 2014 #4

    mfb

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    Did you draw a sketch?
    In principle, you don't need that, if you use the cross-product..

    Sure it does.
     
  6. May 21, 2014 #5
    Yeah, I drew a sketch.
    How about ##F_B = ILB \sin\omega t##?
    From my sketch, it seems that all the forces cancel though... hint please :smile:
     
  7. May 22, 2014 #6

    mfb

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    Looks good.

    Then your sketch might be wrong. As I don't have the sketch, I can't say which part.
     
  8. May 22, 2014 #7
    OH wait, would it be:

    ##\tau = IA\times B = IAB\sin (\omega t)##
    ## I(cd)B\sin\omega t##

    Then plug in I from the equation in the original post ? i am fairly confident on this now.
     
  9. May 22, 2014 #8

    mfb

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    Looks good.
     
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