Question

Two long, straight, parallel conductors carry steady currents in opposite directions. Explain the nature of the force of interaction between them. Obtain an expression for the magnitude of the force between the two conductors. Hence define one ampere.

Hint:

The force between two conductors depends on the current in each conductor and the distance between them.

Answer 1

The interaction force between two parallel conductors carrying electric currents arises from the magnetic field generated by each conductor influencing the other. The force is repulsive when the currents flow in opposite directions and attractive when they flow in the same direction.

The magnitude of this force per unit length is quantified by Ampère's force law:
\[F = \frac{\mu_0 I_1 I_2}{2 \pi d},\]
wherein:
- \( I_1 \) and \( I_2 \) represent the currents in the respective conductors,
- \( d \) denotes the separation distance between them,
- \( \mu_0 \) signifies the permeability of free space.

The definition of one ampere is established as the current that, when passed through two parallel conductors separated by one meter, generates a force of \( 2 \times 10^{-7} \, \text{N/m} \) on each conductor.