Separation distance between wires - Magnetic fields

[SimonSays]

Homework Statement

http://i.imgur.com/mgIkS.png
Two long parallel wires carry currents of 2.03 A and 8.83 A. The magnitude of the force per unit length acting on each wire is 4.49*10^5 N/m. Find the separation distance of the wires expressed in millimeters.

Homework Equations

I'm not entirely sure.

The Attempt at a Solution

I thought that I would need to use the formula:
http://latex.codecogs.com/gif.latex?F_{21}=(\mu_0*I_1*I_2*L )/(2\pi d)
I don't have L however, so how do I solve for d?

 

[rickz02]

Actually you have the right formula, just understand the parameters involved and relate to the given problem.

Hint: "The magnitude of the force per unit length acting on each wire is 4.49*10^5 N/m."

 

[SimonSays]

So are you suggesting that L=1?
Edit: I tried it with L=1 and it worked. Thanks!

 

[rickz02]

We'll you can say that, but I can also say L=2 and my F = 2.245x10⁵ N/m.

What I want you to understand is that you don't need to know L as you are readily given with F/L.

 

[rwisz]

I can provide a response to this question by explaining the relevant concepts and equations involved in solving for the separation distance between the wires.

Firstly, the force per unit length acting on a wire due to a magnetic field is given by the equation:

http://latex.codecogs.com/gif.latex?F=\frac{\mu_0}{2\pi}I_1I_2\frac{L}{d}

Where μ0 is the permeability of free space, I1 and I2 are the currents in the two wires, L is the length of the wires, and d is the separation distance between the wires.

In this problem, the force per unit length is given as 4.49*10^5 N/m and the currents in the wires are 2.03 A and 8.83 A. Therefore, we can rearrange the equation to solve for the separation distance d:

d = (μ0 * I1 * I2 * L) / (2π * F)

We do not have the length of the wires, but we can assume that they are long enough for the magnetic field to be considered uniform along their length. In this case, the length of the wires will not affect the separation distance and we can set it to any value.

Therefore, we can use the given values to calculate the separation distance d in meters:

d = (4π * 10^-7 * 2.03 * 8.83 * 1) / (2π * 4.49*10^5) = 1.62*10^-6 m

To express this in millimeters, we can multiply by 1000 to get the final answer of 1.62*10^-3 mm.

In conclusion, the separation distance between the wires is 1.62*10^-3 mm. This shows that even with relatively small currents, the force per unit length can be quite large, highlighting the strong relationship between separation distance and magnetic fields.