In standard household wiring, parallel wires about 1 cm apart carry currents of about 15 A.
What’s the force per unit length between these wires?

Given Information:

distance between wires = d = 1 cm = 0.01 m

Current in wire_1 = I₁ = 15 A

Current in wire_2 = I₂ = 15 A

Required Information:

Force per unit length = F/L = ?

F/L = 0.0045 N/m

Explanation:

When two parallel wires carrying a current I₁ and I₂ are separated by a distance d then the force between these wires is given by

F/L = μ₀I₁ I₂/2πd

Where μ₀= 4πx10⁻⁷ N/A² is the permeability of free space

This force will be attractive when the current in the two wires are in the same direction otherwise, the force will be repulsive.

F/L = 4πx10⁻⁷*15*15/2π*0.01

F/L = 0.0045 N/m

Therefore, the force per unit length between these two wires is 0.0045 N/m

If we know the length of the wires then we will get the force in Newtons.