Write an expression for force per unit length between two long current carrying wires, kept parallel to each other, in vacuum and hence define an ampere, the SI unit of current.

The force per unit length between two long, parallel current-carrying wires can be expressed using the formula:

Formula for Force per Unit Length

The expression is given by:

F/L = (μ₀/2π) * (I₁ * I₂) / d

• F = force between the wires
• L = length of the wires
• μ₀ = permeability of free space (vacuum)
• I₁ and I₂ = currents in the two wires
• d = distance between the wires

Defining the Ampere

The ampere, symbolized as A, is the SI unit of electric current. It is defined based on the force experienced between two parallel conductors. Specifically, one ampere is the current that, when flowing through two infinitely long, parallel wires separated by one meter in a vacuum, produces a force of 2 × 10⁻⁷ newtons per meter between them.

This definition establishes a fundamental relationship between electric current and magnetic forces, highlighting the interconnectedness of electricity and magnetism in physics.