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Magnetic forces

  1. Feb 6, 2014 #1
    Hello,

    i'm working through some prep required for my lab course and having some trouble understanding an equation. We're asked to show it's derivation and I think i've done this but the script itself is a bit ambigous about how to get there.

    1. The problem statement, all variables and given/known data

    The magnetic force of mutual repulsion between the wires is [itex]F = \frac{\mu_{0} I^{2} L}{2 \pi r}[/itex]

    Ideally this force should balance the weight of the rider, however there may also be a contribution from the earths magnetic field, which will add a force [itex]B_{e} IL[/itex]

    By replacing [itex]I^{2}[/itex] with [itex]I_{1}I_{2}[/itex] the effect of the external fields should cancel.
    2. Relevant equations



    3. The attempt at a solution

    Depending on the direction of the current, the earth's magnetic field is either contributing to or opposing the force due to the magnetic field of the wire, so

    [itex]F_{1} = \frac{\mu_{0} I_{1}I_{2} L}{2 \pi r} + B_{e} IL[/itex]

    [itex]F_{2} = \frac{\mu_{0} I_{1}I_{2} L}{2 \pi r} - B_{e} IL[/itex]

    [itex] F_{1} + F_{2} = \frac{\mu_{0} I_{1}I_{2} L + \mu_{0} I_{1}I_{2}L}{2 \pi r}[/itex] (earths magnetic field cancels)

    [itex] 2F = \frac{2(\mu_{0} I_{1}I_{2} L) }{2 \pi r}[/itex]

    [itex] F = \frac{\mu_{0} I_{1}I_{2} L}{2 \pi r}[/itex] this is the equation I wanted to reach. Are my steps to get here ok? I don't really know how to put into words the importance of substituting I^2 for I1I2...

    Since this force should balance the weight of the rider we can say;

    [itex] mg = \frac{\mu_{0} I_{1}I_{2} L}{2 \pi r}[/itex] and rearrange to get

    [itex]I_{1}I_{2} = (\frac{g2 \pi r}{\mu_{0} L}m[/itex] Which is what I want to plot a graph of)

    Apologies if this is a bit of a vague post, but I don't have much practice of lab work and I don't know if my steps count as showing why the magnetic field of the earth cancels due to the substitution of I^2 that I made. I do include a few more steps in the algebra in my book, showing explicitly the force due to the earths magnetic field cancelling etc.

    Thanks,

    BOAS
     
  2. jcsd
  3. Feb 6, 2014 #2

    BvU

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    You're not getting much quick help here. Could it be the problem formulation is somewhat unclear to others ? They may know about forces between current carrying wires, but who is riding them ?
    You are to do some experiment, measure something and plot the results in a smart way, right ?
     
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