Question

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.

Answer 1

The force acting per unit length of each wire in a vacuum, where two infinitely long straight parallel current-carrying conductors are separated by a distance r, is determined by:

f = `F/L`

= `mu_0/(2 pi)*(I_1 I_2)/r`

If I₁ = I₂ = 1 A and 

r = 1 m,

then,

f = 2 × 10⁻⁷ N/m

The current flowing in each of two long, straight, and parallel wires placed exactly 1 metre apart in a vacuum so that there is a force of 2 × 1⁰⁻⁷ N per unit length acting on the wires.