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Proving an expression / help with defining electric current

  1. Apr 10, 2016 #1
    1. The problem statement, all variables and given/known data
    http://imgur.com/AotzH28
    Two long, straight conducting wires with linear mass density λ are suspended from cords so that they are each horizontal, parallel to each other, and a distance d apart. The back ends of the wires are connected to each other by a slack,low-resistance conducting wire. A charged capacitor ( capacitance C) is now added to the system; the positive plate of the capacitor(initial charge +Q) is now connected to the front end of one of the wires, and the negative plate (initial charge -Q) is connected to the other end of the wire. Both of these connections are also made of slack, low-resistance wires. when the connection is made, the wires are pushed aside by the repulsive force between the wires,and each wire has an initial velocity of magnitude V0
    Assume that the time constant for the capacitor to discharge in negligible compared to the time it takes for any displacement in the position of the wires to occur.

    a) Show that the initial speed of either wire is given by
    v0=(μ0Q02)/(4πλRCd)

    2. Relevant equations
    F=ILB
    B=(μ0I)/(2πr)


    3. The attempt at a solution
    F=ILB
    F/L=IB
    F/L=(μ0I2)/(2πr)

    But here's where I'm stuck.
    I tried working it out from here and the answer ends up being wrong.
    The next step is
    F/L=(μ0I2)/(4πr)
    which is gotten from isolating I2/2 and putting it back into the equation, but I don't see how that's exactly done.
    Any tips?
     
  2. jcsd
  3. Apr 10, 2016 #2

    gneill

    User Avatar

    Staff: Mentor

    I see that the given solution has an R in it. Presumably this is the electrical resistance of the wire path. This leads me to believe that you're meant to consider that the current decays over some short time dictated by the RC time constant.

    Why not start by writing an expression for ##I(t)##. Incorporate that into your expression for the force per unit length on the wires. Then think about how you might turn that force per unit length into an acceleration.
     
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