1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Magnetic forces

  1. Feb 6, 2014 #1

    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.


  2. jcsd
  3. Feb 6, 2014 #2


    User Avatar
    Science Advisor
    Homework Helper
    2017 Award

    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 ?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: Magnetic forces
  1. Magnetic Force (Replies: 7)

  2. Magnetic force (Replies: 3)

  3. Magnetic force. (Replies: 18)

  4. Magnetic Force (Replies: 1)