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Induced emf of Sliding Wire Down Rails

  1. Mar 18, 2015 #1
    1. The problem statement, all variables and given/known data
    [This is the best image I could find]
    e_48_3_008_p1.jpg
    The link on the bottom part of the rails is now removed creating two parallel wires that are not connected (so no longer U shaped but just two rails).
    Now a wire of length L, mass m and resistance R slides without friction down parallel conducting rails of negligible resistance. The rails make an angle of θ with the horizontal and a uniform magnetic field B points vertically upward throughout the region. If the wire starts from rest, what emf will be observed across it after it travels 0.05m?

    2. Relevant equations
    I don't know if any that I know apply

    3. The attempt at a solution
    So if the bottom part of the rails were there, I would just need to apply Faraday's Law and be done: (e.g. ε = -dΦB/dt; ΦB = B dot A ∴ ε = BLvcosθ, then to solve for v we just set force of gravity equal to magnetic force and substitute back into original equation)
    However, the bottom part of the rails is not there, and I don't know how to start. I would make a guess and say ε = 0 since there is no loop
     
  2. jcsd
  3. Mar 18, 2015 #2

    BvU

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    Hello BM, and welcome to PF :smile: !

    Not much to go on then, eh ? No equations and no bottom part, so the whole attempt at solution goes down the drain !

    Let me try to verify that: ever heard of the Lorentz force ? If yes, then you do know one that applies !

    In the moving wire, there are free charge carriers and they too are moving through a magnetic field. So they will go where the Lorentz force forces them !
    And they can't go far if the loop isn't closed, right ? Because when they are pushed together one way, they build up an electric field in the conductor. Stops them from moving (because the Lorentz force is now zero), But that E field constitutes a potential difference, an emf ! Just like in Faraday's law. And you already know what to do when that applies! Isn't that cute ?

    Check out the link between Lorentz force and Faradady's law here.
     
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