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

1. May 24, 2010

### Signifier

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

Note that in the following, 4$$\pi$$ 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$$pi$$)(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$$\pi$$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$$\pi$$)(dL/dr)
This is given. I can rewrite this with my force result to show that T must be greater than F / 2$$\pi$$.

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)