Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Tension at which a loop of wire will break

  1. May 24, 2010 #1
    1. The problem statement, all variables and given/known data

    Note that in the following, 4[tex]\pi[/tex] means 4 * pi not 4 ^ pi...

    A circular loop of wire of self-inductance L and radius r carries a current I. If T is the tension in the wire for which it will break, show that T must be greater than (I2/4[tex]pi[/tex])(dL/dr)

    2. Relevant equations
    Well, the magnetic energy is U = (1/2)I2L. F equals grad U. The circumference of a circle of radius r is 2[tex]\pi[/tex]r. We are assuming a constant current I and a deformable wire.

    3. The attempt at a solution
    The force that tends to increase the radius of the loop is F = (1/2)I2(dL/dr). My problem is that I am not sure how to relate this isotropic outward force to tension in the wire. If I have a wire loop, and I exert a "magical force" F that is a function of the radius of the loop r, F(r), what is the tension that develops in the loop?

    T must be greater than (I2/4[tex]\pi[/tex])(dL/dr)
    This is given. I can rewrite this with my force result to show that T must be greater than F / 2[tex]\pi[/tex].

    I think I just need someone to talk to me about tensions in curves. I know I have a book that talks about this somewhere, but I can't find it. BTW this homework problem is from Wangness, Electromagnetic Fields 2nd edition, chapter 18 page 296.

    Thank you!
    (Please forgive me for the latex formatting issues)
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted