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Induced Current in a Circuit

  1. Nov 3, 2008 #1
    1. The problem statement, all variables and given/known data
    A two-loop wire circuit is 53.4069 cm wide
    and 35.6046 cm high. The wire circuit in
    the figure is located in a magnetic field whose
    magnitude varies with time according to the
    expression B = (0.001 T/s) t and its direction
    is out of the page.

    Assume The resistance per length of the
    wire is 0.113 Ohm/m.

    [​IMG][​IMG]

    When the magnetic field is 0.2 T, find the
    magnitude of the current through middle leg
    PQ of the circuit. Answer in units of μA.


    2. Relevant equations
    [tex]
    \mathcal{E} = -A\frac{dB}{dt}
    [/tex]

    [tex]
    \mathcal{E} = I R
    [/tex]


    3. The attempt at a solution
    [tex]
    \mathcal{E} = -(0.356046m)(0.356046m)(0.001T/s) = -1.267687541\times 10^{-4} v
    [/tex]

    [tex]
    \mathcal{E} = -(0.178023m)(0.356046m)(0.001T/s) = -6.338437706\times 10^{-5} v
    [/tex]

    [tex]
    \frac{(-1.267687541\times 10^{-4}v) - (-6.338437706\times 10^{-5}v)}{0.113}
    [/tex] = -560.92 μA

    I might have messed up on the signs, and also I'm not sure how "When the magnetic field is 0.2 T" applies to my equations.
     
  2. jcsd
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