Question

Obtain expression for the force between two infinitely long straight parallel conductors carrying current. Hence define ‘ampere’ the SI unit of electric current.

Answer 1

Consider two infinitely long straight conductors a & b carrying currents Ia & Ib respectively are separated by a distance ‘d’. The conductor ‘a’ produces the same magnetic field Ba at all points along the conductor ‘b’.

Ba = \(\frac{\mu_0 I_a}{2\pi d}\)  ......(1)

The conductor ‘b’ experiences a force F_ba

F_ba = B_aLI_b = \(\frac{\mu_0 I_a I_bL}{2\pi d}\)

where L = length of the conductor

\(\frac{F_{ba}}{L} = \frac{\mu_0 I_aI_b}{2\pi d}\)

Similarly one can show that F_ba = -F_ab (A) ampere. The currents flowing through two infinitely long parallel conductors separated by 1m distance is 1 ampere if they experience a force of 2 X 10^–7N per unit length in air or vaccum.