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Homework Help: Repeat Q: Ignore. Show what the magnitude of induced emf

  1. Nov 19, 2011 #1
    Show what the magnitude of induced emf

    1. The problem statement, all variables and given/known data

    Consider a magnetic field B = K(x3z2,0, -x2z3)sinωt in the region of interest, where K and ω are positive constants and t is variable time. Show that the magnitude of the induced emf around a circle R in the plane z = a with its center at x = 0, y = 0, z = a is:
    ε = (K/4)∏a3R4ωcosωt

    2. Relevant equations

    Fluxb = ∫B . dA

    3. The attempt at a solution

    Since the normal vector points in the k direction, we only have to worry about Bz.

    ∫Bzdydx. So -∫∫x2a3dydx.

    The make the change to polar:

    -aK3∫∫(rcosθ)2r dr dθ = -(K/4)a3R4∫cosθsinψt dθ.

    This doesn't get me anywhere.
    Last edited: Nov 19, 2011
  2. jcsd
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