There Are Two Wires With Current Flowing, Find The Distance Between Them Caused By Magnetic Repulsion.

Question

A wire 2 m long and weighing 0.08 N/m is suspended directly above a second wire. The top wire carries a current of 30 A and the bottom wire carries a current of 60 A. Find the distance of separation between the wires such that the top wire will be held in place by magnetic repulsion.

If two wires have a magnetic repulsion, the current must be going the opposite direction. I think I use formula:

F/L = [(4pix10^-7) * (I(1)) * (I(2))] / ((2pi) * (d))

Do I suppose to add the forces together? How do I do this problem? Please Help Me.

Answer 1

The formula looks OK

The forces the two wires exert on each other are equal and opposite.

The force required to suspend wire 1 is = 0.16 N

Solve for d:

d = 2 X 10^-7 * i1 * i2 * L / F

d = 2 x 10^-7 * 30 * 60 * 2 / 0.16 = 0.0045 m