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Induced Current question

  1. Mar 25, 2009 #1
    1. The problem statement, all variables and given/known data
    The rectangular loop shown has resistance 20.0 mΩ.
    Determine the induced current in the loop at the instant shown.
    Answer: 66.7µA
    http://img264.imageshack.us/img264/7386/picture1nlz.png [Broken]


    2. Relevant equations

    induced emf = |d(flux)/dt|
    I = emf / R

    3. The attempt at a solution
    I am so lost as to what to do... and I am so desperate.. If you could tell me the steps to solve this question, i would appreciate it very much.
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Mar 25, 2009 #2

    berkeman

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    Staff: Mentor

    Show us the Biot-Savart Law (that gives you the B(r) around the wire). Then show us the rest of the solution. I have to give myself an infraction now for giving too big of a hint...
     
    Last edited: Mar 25, 2009
  4. Mar 25, 2009 #3
    Well... the problem is that.. I got this far:

    emf = | d(flux)/dt |
    = dB * A / dt
    = dB (0.04*0.01) / dt
    = dB (4*10^-4) / dt

    but i do not know how to get dB...;
    in other words, i am totally lost.


    I have B(r) = u0I/(2*pi*r)

    This is my first time seeing this type of question.. and I am very confused as to what I'm doing.

    Sorry if it sounds stupid.
     
  5. Mar 25, 2009 #4

    berkeman

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    Staff: Mentor

    The loop is moving with respect to the wire. So the B(t) through the loop will be changing, since the B is weaker the farther you get away from the wire. Write an equation based on the Biot-Savart Law for the flux throught the loop as a function of radius, and work from there...
     
  6. Mar 25, 2009 #5
    Which radius should I use? The distance from the wire to the the inner side of the loop or the outer side of the loop?
     
  7. Mar 25, 2009 #6

    berkeman

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    Staff: Mentor

    You need to integrate over the loop radius.
     
  8. Mar 31, 2011 #7
    I know this is old but i'm working on the exact same question.

    So far i have this:
    [PLAIN]http://www.texify.com/img/%5CLARGE%5C%21%5Cphi%20%3D%20B%20%5Cbullet%20dA%20%5C%5CB%20%3D%20%5Cmu_0%20I/%20%282%20%5Cpi%20r%29%20%5Ctextrm%7B%20by%20ampere%27s%20law%7D%20%5C%5C%5Cphi%20%3D%20%5Cmu_0%20I/%20%282%20%5Cpi%20r%29%5Cbullet%20dA%20%5C%5C%5Cphi%20%3D%20%5Cmu_0%20I/%20%282%20%5Cpi%20r%29%20L%20dr%20%5C%5C%5Cphi%20%3D%20%5Cint_a%5Eb%20%5Cmu_0%20I/%20%282%20%5Cpi%20r%29%20L%20dr%20%5C%5C%5Cphi%20%3D%20%5Cfrac%7B%20%5Cmu_0%20I%20%5Cln%7B3/2%7D%7D%7B%5Cpi%7D.gif [Broken]


    Where the bounds of integration are b = 0.02 and a = 0.03 and L= 4.0cm from the picture. This is where i get lost. I wanted to use faraday's law to use:

    [PLAIN]http://www.texify.com/img/%5CLARGE%5C%21%5Ceps%20%3D%20%5Cmid%20%5Cfrac%7Bd%20%5Cphi%7D%7Bdt%7D%20%5Cmid.gif [Broken]

    Am i just totally going about this the wrong way by trying to use flux, and i have to use biot savart law?
     

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    Last edited by a moderator: May 5, 2017
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