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 force between two parallel conductors carrying currents is due to the magnetic field produced by one conductor acting on the other. The force is repulsive if the currents are in opposite directions and attractive if the currents are in the same direction. The magnitude of the force per unit length between two conductors is given by Ampère's force law: \[ F = \frac{\mu_0 I_1 I_2}{2 \pi d}, \] where: - \( I_1 \) and \( I_2 \) are the currents in the two conductors, - \( d \) is the distance between them, - \( \mu_0 \) is the permeability of free space. One ampere is defined as the current that, when flowing through two parallel conductors one meter apart, produces a force of \( 2 \times 10^{-7} \, \text{N/m} \) on each conductor.