Two straight and parallel wires of length 1.0 m carry a current - the first carries a currecnt of 9.0 A while the other wire carries a current of 4.0 A. What distance must separate the two straight and parallel copper wires if the force between them is to be 6.0 x 10-6 N?

My Answer:
Magnetic field created by the second wire:
Fm = IlBsinθ
6*10-6= (4)(1)Bsin(90)
6*10-6= (4)B
B =6*10-6/4
B=1.5*10-6 T

This means the first wire will be in a magnetic field of 1.5*10-6 T.

First wire:
B=μ I / 2π r
r= μ I / 2πB
r=(4π*10-7)(9)/ 2π(1.5*10-6)
r= (1.130973355*10-5)/(9.424777961*10-6)
r=1.9999979

The wires must be separated a distance of 1.2m.

Is this correct? thanks for your help.

Thanks a lot for your help, drwls. I just have one more problem. Why did you substitute (2*10-7) for μ. I thought μ= (4pi*10-7). If I substitute(4pi*10-7), my answer come out correct. Did you mean to cancel the 2pi in the numerator and denominator. Could you help me understand? Thanks again.

I believe your formula is incorrect.

F/L = μ I1*I2/(2 pi r)
= 2*10^-7 * 36/(2*pi*r) = 6*10^-6 N

r = [1/(2 pi)]*6*10^-1

That is about 0.095 meters

Reference:
http://theory.uwinnipeg.ca/physics/mag/node10.html

Your calculations are mostly correct, but there is a small error in your final calculation. Let's go through the steps again to find the correct result:

First, calculate the magnetic field created by the second wire:

B = μ0 * I / (2π * r)
B = (4π * 10^-7) * 4 / (2π * r)
B = (2 * 10^-7) / r

Now, equate this magnetic field to the force between the wires:

F = B * I * L
6 * 10^-6 = (2 * 10^-7) / r * 9 * 1
6 * 10^-6 = (2 * 10^-7) * 9 / r
r = (2 * 10^-7) * 9 / (6 * 10^-6)
r = (1.8 * 10^-6) / (6 * 10^-6)
r = 0.3 m

Therefore, the correct distance to separate the two wires is 0.3 meters or 30 centimeters.

Your calculations are mostly correct, but there seems to be a mistake in the final result. Let's go through the calculations to determine the correct answer.

To find the magnetic field created by the second wire, we can use the formula:

Fm = IlBsinθ

From the given information, we know that Fm = 6.0 x 10^(-6) N, I = 4.0 A, L = 1.0 m, and sinθ = 1 (as the wires are parallel). Substituting these values into the formula:

6.0 x 10^(-6) N = (4.0 A)(1.0 m)(B)(1)

B = 6.0 x 10^(-6) T

Now, let's move on to the first wire. The magnetic field created by the second wire is also the magnetic field experienced by the first wire. Using the formula:

B = (μ0 I) / (2πr)

We can rearrange the equation to solve for r:

r = (μ0 I) / (2πB)

Substituting the given values:

r = (4π x 10^(-7) T*m/A)(9.0 A) / (2π x 6.0 x 10^(-6) T)

Simplifying:

r = (3.6 x 10^(-6) T*m) / (1.2 x 10^(-5) T)

r = 0.3 m

Therefore, the correct distance that must separate the two wires is 0.3 meters, not 1.2 meters as calculated in your answer.

Note: The equation used for the force between two parallel wires carrying current can be derived from the Biot-Savart law and the right-hand rule. It is important to understand the derivation process in order to apply the formula correctly.