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Homework Help: Current of Sliding Rod

  1. May 16, 2015 #1
    1. The problem statement, all variables and given/known data

    If the U-shaped conductor in the figure has resistivity ρ (in Ω.m), whereas that of the moving rod is negligible, find the current I at time t. Assume the rod has length L, starts at the bottom of the U at t = 0, and moves with uniform speed v in the constant magnetic field B shown in the figure. The cross-sectional area of the rod and all parts of the U is A (in m2). Express your answer in terms of the given quantities.

    2. Relevant equations

    I = magnetic flux / Resistance

    Resistance = p*L/A where p is the resistivity

    3. The attempt at a solution

    I = B*A*v/p*(L/A)

    The current is equal to the magnetic field times the Area times the velocity, divided by Resistance (which is the resistivity times the Length times the Area)

    What am I missing here because that formula that I calculated is wrong?
  2. jcsd
  3. May 16, 2015 #2
    instead of going for that formula, go for the basic definition if induced EMF. As the rod moves with a velocity v, what is the emf induced on it?
  4. May 16, 2015 #3
    Emf would be : B*A*v

    So then where does the resistivity come in?
  5. May 16, 2015 #4
    no. emf is not BAv. Its Blv where l is the length of the rod. think about it. try to derive it.
  6. May 16, 2015 #5
    I'm taking an algebra based physics course so I'm not too comfortable with deriving but looking at an example of the derived form:

    so after deriving the Emf equation, Emf = B L v and I would them be B L^2 v / p L/A ?
  7. May 16, 2015 #6

    Here is the picture for the problem, sorry forgot to post it
  8. May 16, 2015 #7


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    How did L become L2.

    Also, note that the resistance is in the U-shaped conductor. So, when using R = pL/A you need to consider the length of the U-shaped portion of the circuit. So, the L here is not the same as the L for the length of the moving rod. The length of the U-shaped portion will depend on the time t.
  9. May 16, 2015 #8
    I'm confused with what you would do with the time t. If the length changes based on t then can I just multiply the length by t?
  10. May 16, 2015 #9


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    In the figure below, let x be the distance the rod has traveled. Can you express the length of the U-shaped portion of the circuit in terms of x and L? Then you can express x in terms of t.

    Attached Files:

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