Two straight and parallel wires of length 1.0 m carry a current — the first carries a current 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 × 10−6 N?

This post was by accident sorry the answer is not 5.

To find the distance between the two wires, we can use Ampere's Law, which states that the force between two parallel wires is directly proportional to the product of their currents and inversely proportional to the distance between them.

The formula to calculate the force between two parallel wires is given by:
F = (μ₀ * I₁ * I₂) / (2π * d),

where F is the force between the wires, I₁ and I₂ are the currents in the first and second wires, d is the distance between the wires, and μ₀ is the permeability of free space, which has a constant value of 4π × 10^(-7) T·m/A.

Given:
I₁ = 9.0 A (current in the first wire)
I₂ = 4.0 A (current in the second wire)
F = 6.0 × 10^(-6) N (force between the wires)

Plugging in the values into the formula, we have:
6.0 × 10^(-6) = (4π × 10^(-7) * 9.0 * 4.0) / (2π * d).

Simplifying the equation:
6.0 × 10^(-6) = (4π × 10^(-7) * 36.0) / (2π * d).
6.0 × 10^(-6) = (1.44 × 10^(-6)) / d.

To solve for d, we can rearrange the equation:
d = (1.44 × 10^(-6)) / (6.0 × 10^(-6)).

Dividing the values:
d = 0.24 m.

Therefore, the distance between the two wires must be 0.24 meters in order for the force between them to be 6.0 × 10^(-6) N.