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Conducting slidewire see system-Faraday's Law

  1. May 5, 2015 #1
    1. The problem statement, all variables and given/known data

    A conducting slidewire system is set up as shown. The sliding wire has mass m and electrical resistance R and falls under gravity as shown. The fixed wire loop has zero resistance and lies perpendicular to a uniform magnetic field B shown pointing into the page.
    i) Use Faraday's Law to determine the maximum velocity of the slidewire.
    ii) How much power is dissipated at the peak velocity?

    2. Relevant equations

    ɛ=-dФ/dt
    P=(I^2)R

    3. The attempt at a solution
    I defined the area vector as pointing in the same direction as the magnetic field, so
    ɛ=-B(dA/dt)
    In time dt the slidewire moves a distance vdt, giving ɛ=-BLv where L is the width of the slidewire.
    I think I am simplifying the problem too much by simply rearranging for v in this equation and obtaining
    v=-ɛ/BL -should I differentiate in order to maximise v? I feel I am missing something by not including the given mass m.

    For the second part, overall current I=|ɛ|/R, so I=BLv/R
    P=I^2R=(BLv/R)^2/R

    P(dissipated)=(B^2L^2v^2)/R

    Thanks in advance for any help, much appreciated.
     

    Attached Files:

  2. jcsd
  3. May 5, 2015 #2

    BvU

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    But with v=-ɛ/BL you haven't determined v yet, have you !?

    Is there something that stops you from answering e.g. ## v = -{\tfrac 1 2} g t^2 ## ?

    [edit]
    Not so certain my help has helped. Can you enlighten me ?
     
    Last edited: May 6, 2015
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