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Magnetic Induction Through a Moving Wire

  1. Apr 2, 2013 #1
    1. The problem statement, all variables and given/known data
    A very long u-shape conducting wire is placed vertically in a constant magnetic field. The magnetic field is perpendicular to the plane of the wire. The strength of the magnetic field is B = 0.9 tesla. A conducting rod is placed on the wire, as shown in the picture. The length of the rod is 7 m. The rod has a mass of 5 kg and a resistance of 8 Ohm. When the rod is released from rest, it start to slide down but maintain good contact with the u-shape wire. After some time, the rod reaches a maximum velocity and moves constantly thereafter. You can ignore the resistance of the u-shape wire and the friction between the rod and the wire.
    B = 0.9T ; L = 7m ; R = 8Ω ; g= 9.8m/s
    What is the maximum velocity of the moving rod?
    What is the current in the loop when the moving rod reaches maximum velocity?

    2. Relevant equations
    ε= v*L*B
    I=(v*L*B)/R
    F = I*L*B

    or
    F = (v(L*B)^2)/R


    3. The attempt at a solution

    Ok I know that once this wire begins to move it creates an emf and a current. The magnetic force generated is going to counteract my force of gravity. My assumption is that when it reaches its maximum velocity the F will be 9.8 as well since it can no longer change.
    So:
    F = 9.8N?
    I've tried plugging in from here and have not been able to get a correct answer, where am I going wrong?
    9.8 = I(7)(0.9) thus I = 1.56A

    1.56 = (v(7)(0.9))/8 thus v = 1.97m/s
     

    Attached Files:

    Last edited: Apr 2, 2013
  2. jcsd
  3. Apr 2, 2013 #2
    As soon as I posted this I remembered that the F is ACTING on MASS. This makes my F = 49N
    D'oh!
    I'll leave this here I guess.
    Plugging in it all worked out smoothly :)
     
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