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Induced Voltage of Faraday's Disk

  1. Feb 3, 2010 #1
    1. The problem statement, all variables and given/known data
    The problem can be found http://whites.sdsmt.edu/classes/ee382/homework/382Homework3.pdf" [Broken]. It is the first one.


    2. Relevant equations
    [tex]V_{emf} = \oint_L (\vec{\boldsymbol u} \times \vec{\boldsymbol B}) \cdot d\vec{\boldsymbol l}[/tex]


    3. The attempt at a solution
    [tex]\vec{\boldsymbol u} = \rho\omega\hat{\boldsymbol a}_{\Phi}[/tex]

    [tex]\vec{\boldsymbol B} = B_0\hat{\boldsymbol a}_{z}[/tex]

    [tex]d\vec{\boldsymbol l} = d\rho\hat{\boldsymbol a}_{\rho}[/tex]

    [tex]\vec{\boldsymbol u} \times \vec{\boldsymbol B} = \rho\omega\hat{\boldsymbol a}_{\Phi} \times B_{0}\hat{\boldsymbol a}_{z} = \rho\omegaB_{0}\hat{\boldsymbol a}_{\rho}[/tex]

    [tex]V_{emf} = \oint_L(\vec{\boldsymbol u} \times \vec{\boldsymbol B}) \cdot d\vec{\boldsymbol l} = \oint_{L}\rho\omega B_{0}\hat{\boldsymbol a}_{\rho} \cdot d\rho\hat{\boldsymbol a}_{\rho} = \oint^{R}_{0}\rho\omega B_{0}d\rho = \omega B_{0}[\rho^{2}/2]^{R}_{0} = NB_{0}R^{2}/2[/tex]

    I'm pretty certain that this answer is correct. What I'm uncertain of is the polarity of the voltage. Should I add a minus sign in front, or leave it as is?
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
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