Question

Obtain the formula for the magnetic force between two parallel long current carrying conductors and define 1 A of current with its help.

Hint:

The magnetic force between two current-carrying conductors is directly proportional to the product of the currents and inversely proportional to the distance between them. The definition of 1 Ampere is based on this fundamental principle.

Answer 1

The magnetic force between two parallel current-carrying conductors is derived using Ampère's law. The magnetic field generated by one conductor creates a force on the other conductor. The force per unit length between two parallel conductors is given by the formula: \[ F/L = \frac{\mu_0 I_1 I_2}{2 \pi r} \] Where: - \(F\) is the force between the conductors,
- \(L\) is the length of the conductors,
- \(\mu_0\) is the permeability of free space (\(\mu_0 = 4\pi \times 10^{-7}~\text{N/A}^2\)),
- \(I_1\) and \(I_2\) are the currents in the two conductors,
- \(r\) is the distance between the two conductors.
The direction of the force is determined by the direction of the currents in the conductors. If the currents flow in the same direction, the force is attractive. If the currents flow in opposite directions, the force is repulsive.
This formula expresses the force per unit length between two parallel conductors due to the magnetic field produced by one conductor that acts on the other conductor. % Definition of 1 Ampere: Definition of 1 Ampere:
1 Ampere (1 A) is defined as the current that, when flowing through two parallel conductors placed 1 meter apart in a vacuum, produces a force of \(2 \times 10^{-7}~\text{N/m}\) between the conductors. This definition links the concept of current with the magnetic force between conductors, providing a direct method for measuring electric current.