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Contracting Loop in a Magnetic Field (emf and current)

  1. May 17, 2009 #1
    1. The problem statement, all variables and given/known data
    An elastic circular loop in the plane of the paper lies in a 0.71 T magnetic field pointing into the paper. If the loop's diameter changes from 19.3 cm to 7.2 cm in 0.54 s,

    a. what is the magnitude of the average induced emf?
    HELP: Use Faraday's Law and evaluate the rate of change of magnetic flux through the loop.

    b. If the loop's resistance is 2.6 Ω, what is the average induced current I during the 0.54 s?


    2. Relevant equations
    [tex]\Delta[/tex][tex]\Phi[/tex]/[tex]\Delta[/tex]t=emf
    [tex]\Delta[/tex][tex]\Phi[/tex]=magnetic flux = BAcos[tex]\theta[/tex]

    3. The attempt at a solution
    So I used the above equation to find the emf
    [tex]\pi[/tex](.0605)2(.71)/.54 = .0151
    Where the value for r is the amount that the radius changes in the time given.
    This is wrong, and I'm not quite sure what else to try...
     
  2. jcsd
  3. May 17, 2009 #2

    nrqed

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    For the change of area, you must use : [itex] \pi R_i^2 - \pi R_f^2 [/itex]
    where Ri and Rf are the initial and final radii.
    I see what you did (you took the difference of diameter and divided this by 2 to get a radius ) but that does not give the correct change of area.
     
  4. May 17, 2009 #3
    Oh, that makes sense. Thanks!
     
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