A straight, long wire carries a current of 20 A . A second wire carrying an equal amount of current is placed parallel to the first. If the force exerted on a 10 cm length of the second wire is 2.0 10⁻⁵ N , what is the separation between the wires?

Step-by-step solution

The force per unit length between two parallel current-carrying wires is given by F L = ₀ I₁ I₂ 2 d . The total force on a length L of the second wire is F = ₀ I₁ I₂ L 2 d . Given I₁ = 20 A , I₂ = 20 A , L = 10 cm = 0.1 m , and F = 2.0 10⁻⁵ N . Substituting the values into the formula: 2.0 10⁻⁵ = 4 10⁻⁷ 20 20 0.1 2 d 2.0 10⁻⁵ = 2 10⁻⁷ 40 d 2.0 10⁻⁵ = 8 10⁻⁶ d d = 8 10⁻⁶ 2.0 10⁻⁵ = 0.4 m d = 40 cm