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Derive expression for induced voltage and current

  1. Mar 13, 2012 #1
    1. The problem statement, all variables and given/known data

    A circular conducting loop with radius a and resistance R2 is concentric with a circular conducting loop with radius b much greater than a and resistance R1. A Resistance dependent voltage is applied to the larger loop, having a slow sinusoidal variation in time given by V(t) = V0 sin ωt, where V0 and ω are constants with dimensions of voltage and inverse time, respectively. Assuming that the magnetic field throughout the inner loop is uniform (constant in space) and equal to the field at the center of the loop, derive expressions for the potential difference induced in the inner loop and the current i through that loop.

    2. Relevant equations

    Vind=(d/dt)AB
    where A is the area: A=∏a^2
    and B is magnetic field

    I1=V0/R1
    I2=-Vind/R2

    3. The attempt at a solution

    My understanding is that d/dt=ωcos(ωt)
    and B=μ0*I1/(2*∏*b)=μ0*V0/(2*b*∏*R1)

    The answer for Vind=-∏*a^2*μ0*V0*ω*cos(ωt)/(2*b*R1)
    What I don't understand is what happened to ∏ in B=μ0*V0/(2*b*R1)?
     

    Attached Files:

  2. jcsd
  3. Mar 13, 2012 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Check the formula. There should be no pi in the denominator.

    http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/curloo.html

    ehild
     
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