# Force Per Length and Magnitude of a Current

1. May 11, 2010

### hexus0

1. The problem statement, all variables and given/known data
1.A long, thick (cylindrical, solid) wire of radius 3 mm carries a total current of I1 = 100A that is uniformly distributed over its cross-sectional area. The current is in the +z direction. A second, thin wire runs parallel to the axis of the thick wire and is located at a distance of 7 mm from the center of the thick wire (see the figure). Initially there is no current flowing in the second wire (i.e., initially I2 = 0).

A current I2 (of unknown magnitude and direction) is now switched on in the second wire. The resulting force per-unit-length exerted on the second wire is measured to have a magnitude of 0.25 N/m, and the wires feel attractive forces. What is the magnitude and direction of the current I2?

2. Relevant equations

F = ILxB

B = u0I/(2*pi*r)

3. The attempt at a solution
Using F/L = 0.25 N/m, I set that equal to u0I/(2*pi*r)
so
(F/L) = u0I/(2*pi*r)

Solving for I:

I = [(F/L)*(2*pi*r)]/u0

Plugging in the values gave me I = 8750A. My professor has provided the answers for this study guide and the answer is 87.5A. I realized I made this same mistake on my exam and I was also off by 2 decimal places. I also posted this on my professor's forum, but no answer yet (posted earlier this morning). Any help is appreciated!

Thank you!

2. May 11, 2010

### hexus0

Figured out my problem, I was using the wrong equation.

F/L = u0*I1*I2/(2*pi*r)

Solving gives:

I = (F/L)*2*pi*r/(u0*I1)

I = 87.5A

Hope I didn't waste anyone's time and hopefully someone can learn from my mistakes!