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An Eddy Current brake: Check my answer?

  1. Apr 7, 2013 #1
    1. The problem statement, all variables and given/known data

    Refer to Figure attached.

    A disk of conductivity σ and thickness b rotates around an axis through its center with a magnetic field B applied perpendicular to the plane of the disk over a small area a2. Find the approximate torque tending to slow the disk at the instant its angular velocity is ω.

    2. Relevant equations
    3. The attempt at a solution

    [itex]\xi = -B \frac{dA}{dt} [/itex]

    [itex] = -B a \frac{da}{dt} [/itex]

    (Right here ^ Can I do this?)

    [itex] = -B a v [/itex]

    [itex] = -B a \omega dr [/itex]

    [itex] \Rightarrow \int^{r+a/2}_{r-a/2} -B a \omega dr [/itex]

    [itex] = - B a^2 \omega [/itex]

    And

    [itex] R = \frac{L}{\sigma A} = \frac{a}{\sigma ab} = \frac{1}{\sigma b}[/itex]

    -----
    -----

    Thus

    [itex]F = i a \times B[/itex]

    [itex] = \frac{\xi}{R} a \times B[/itex]

    [itex] F = - B^2 a^2 \omega \sigma b [/itex]

    -----
    -----

    [itex]\tau = \int F dr[/itex]

    [itex]\tau = - B^2 a^2 \omega \sigma b \int^{r+a/2}_{r-a/2} dr[/itex]

    [itex]\tau = - B^2 a^3 \omega \sigma b[/itex]
     

    Attached Files:

    Last edited: Apr 7, 2013
  2. jcsd
  3. Apr 7, 2013 #2
    I think I've handled my integrals poorly...
    will revise.
     
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