Question

State the expression for the force per unit length between two infinitely long parallel conductors carrying current and hence define the SI unit of current.

Answer 1

Imagine two straight, indefinitely long wires that are spaced apart in a vacuum by a length of s. When the conductors' steady currents, I1 and I2, are flowing in the same direction, they attract one another, and when they are flowing in the opposite way, they repel one another. Each conductor's force per unit length is

`F/l = (μ_0/(4π)) (2I_1I_2)/s`

Using SI units, μ₀/4π = 10⁻⁷ N/A² and, if I₁ = I₂ = 1 A and s = 1 m, then

`F/l = 2 xx 10^-7` N/m

In SI, this equation is the defining relation for the ampere.

The ampere is the continuous current that, given two infinitely long, straight parallel wires spaced one meter apart in a vacuum, would result in a force of 2 × 10⁻⁷ newtons per meter acting on each conductor.