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Induced Emf in Rectangular Loop Problem

  1. Jun 15, 2011 #1
    1. The problem statement, all variables and given/known data
    "You push a rectangular loop of width .2m, length .8 m, and resistance R=200[itex]\Omega[/itex] into a magnetic field (out of page) Bout=.4 T and a speed v=.2 m/s. The long side of the rectangle is parallel to the x axis. What is the current flowing in the loop?"

    2. Relevant equations

    I think I should use:
    Ohm's Law - [itex]\Delta[/itex]V=IR
    3. The attempt at a solution
    Using the equation emf=vBl, I did emf=(.02)(.8)(.4)=.0064.
    Then I said that emf=[itex]\Delta[/itex]V, so using Ohm's Law I did [itex]\frac{.0064}{200\Omega}[/itex] and got 3.2 x 10-5 A as my answer.

    My problem is that the only problems we've worked are for circular loops and I'm not sure what length to use for l.
  2. jcsd
  3. Jun 16, 2011 #2

    Andrew Mason

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    Your equation is derived from Faraday's law. So apply Faraday's law explicitly:

    [tex]emf = \oint \vec{E}\cdot d\vec{s} = \frac{d\phi}{dt} = B\frac{dA}{dt}[/tex]

    All you have to do is work out dA/dt, the rate of change of the area enclosed by the loop. If l is the distance along the x axis through which you have pushed the loop and w is the width of the loop what is dA/dt?

  4. Jun 16, 2011 #3
    How would I do this algebraically?
  5. Jun 16, 2011 #4

    Andrew Mason

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    Since dA = wdx and w is constant, then dA/dt = w(dx/dt) = wv

    So emf = Bwv

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