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Difficult inductance + torque rolling rail problem

  1. Nov 24, 2013 #1
    1. The problem statement, all variables and given/known data
    ykL6cA1.png


    2. Relevant equations
    [tex]F = I\vec{l} \times \vec{B}[/tex]
    [tex]\varepsilon = BLv[/tex]


    3. The attempt at a solution

    Every direction i go seems real wrong


    [tex]F = I\vec{l} \times \vec{B}[/tex]

    [tex]F = \frac{\varepsilon \vec{l} \times \vec{B}}{R}[/tex]
    [tex]F = \frac{\varepsilon LB}{R}[/tex]
    [tex]ma = \frac{VLB}{R}[/tex]
    [tex]v = \frac{VLB}{mR}t[/tex]


    while the math seems to all be good here, this implies like every answer after is going to be infinity which seems plain wrong.. I assume I should havea current from the battery versus a current induced and thus have two forces. but things get messy and I can never get a v just in terms of t when I mess with it in this direction. thanks for any help
     
  2. jcsd
  3. Nov 24, 2013 #2

    haruspex

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    Not quite. The motion of the cylinder through the field will induce a "back emf". I'm no expert in this area, but my guess is that the cylinder will cease to accelerate when the back emf equals and cancels the applied emf.
     
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