Magnetic force created by one wire over another

[Parad0x88]

Homework Statement

Two wires, each having a weight per unit length of 10^–4 N/m, are strung parallel, one 0.3 m above the other. If the wires carry the current of same magnitude, how great must the current in each wire be for the magnetic field due to the lower conductor to balance the weight of the upper conductor? What have to be the directions of the two currents for that to work?

Homework Equations

Since we are not given any length, we must work per unit of length, in this case meters.

Weight = mass X gravitational acceleration.

Since we are already given the weight, we simply must find the equivalent force to create an equilibrium.

We also know I₁ = I₂

F₁ = (μ₀I₁I₂)/(2pi X a)

The Attempt at a Solution

Simply solve for I, since I₁ = I₂, we can re-write:

10^-4 N = (μ₀I²)/(2pi X a)

 

[AJ Bentley]

OK, so far, so good. So what's the answer?

 

[Parad0x88]

OK, so far, so good. So what's the answer?

Oh well I had assumed if the formula was good I wouldn't have to go all the way here, but here goes:

(4pi X 10^-7 X I²) / (2pi X 0.3)

F_B = (2 X 10^-7 X I²) / .3

F_B = 6.667 X 10^-6 X I²

I² = 10^-4 / 6.667 X 10^-6

I² = 15

I = 3.87

As for the direction, let's see if I can figure this out, and use what you have taught me in the previous problem :D.

We want them to repel each other. If both wires have the same current direction, they would attract each other, therefore one has to flow left to right, and the other right to left

 

[AJ Bentley]

You lost a factor of 10 halfway. Otherwise good.

 

[Parad0x88]

You lost a factor of 10 halfway. Otherwise good.

Awesome, thanks! And yeah you're right, should be 6.667 X 10^-7