Current Between Long Straight Conducting Wires

[futurepocket]

Homework Statement

Two identical long straight conducting wires with a mass per unit length of 25.0 g/m are resting parallel to each other on a table. The wires are separated by 2.5 mm and are carrying currents in opposite directions.

a) If the coefficient of static friction between the wires and the table is 0.035, what minimum current is necessary to make the wires start to move?
b) Do the wires move closer together or farther apart?

Homework Equations

F(b) = ILB
B = muo(0)I/2pi(r)
F(sf) = muo(s)F(n)

The Attempt at a Solution

Okay, so I realized that for the wires to start moving, the force due to the magnetic field has to equal (match) the force of friction, so I equate the two:

F(b) = ILB = muo(s)F(n)

Then, I realize that F(n) = mg

ILB = muo(s)mg

If you divide out the length, you can get the mass per unit length, so you get:

IB = 0.025muo(s)g
I = 0.025muo(s)g / B

I know the equation to solve for the magnetic field, but at which point am I solving it for so I know the radius to use? You can't really use the center between the wires because the currents are in opposite direction and they are equal, so in the center of the two wires, the magnetic field is 0. Any ideas?

Thank you!

 

[anathema]

Dear fellow student,

Thank you for your post and your attempt at solving this problem. You are on the right track in equating the forces of the magnetic field and friction in order to find the minimum current needed to make the wires start to move.

To answer your question about which radius to use in the equation for the magnetic field, you will need to consider the distance between the wires (2.5 mm) and the radius of each wire. Since the wires are parallel and the currents are in opposite directions, the magnetic field due to each wire will cancel out at the center point between them. However, the magnetic field from each wire will still be present at a distance of 2.5 mm from the center point. Therefore, you can use this distance as the radius in the equation for the magnetic field.

I hope this helps! Let me know if you have any further questions.