Question

Define 1 ampere on the basis of the force acting between two parallel current-carrying conductors.

Hint:

1 ampere is defined as the current that produces a force of \( 2 \times 10^{-7} \, \text{N/m} \) between two parallel conductors placed 1 meter apart.

Answer 1

Step 1: Definition of 1 Ampere.
1 ampere is defined as the current that, when flowing through each of two parallel conductors placed 1 meter apart in a vacuum, produces a force of \( 2 \times 10^{-7} \, \text{N} \) per meter of length between the conductors.
Step 2: Explanation.
This definition is based on the force between two current-carrying conductors. The force per unit length between two parallel conductors is given by: \[ F = \frac{\mu_0 I_1 I_2}{2 \pi r} \] where: - \( F \) is the force per unit length, - \( I_1 \) and \( I_2 \) are the currents in the two conductors, - \( r \) is the distance between the conductors, - \( \mu_0 \) is the permeability of free space (\( \mu_0 = 4\pi \times 10^{-7} \, \text{T m/A} \)). For two conductors with a current of 1 ampere each, placed 1 meter apart, the force between them is \( 2 \times 10^{-7} \, \text{N/m} \). This is the basis for the definition of 1 ampere.