Two parallel conductors each carrying a current of 10 mA in opposite directions are placed at a distance 10 cm apart. The force per unit length between two conductors is

$10 × 10^{-4} (μ_0/2π) N/m$

The correct answer is Option (1) → $10 × 10^{-4} (μ_0/2π) N/m$

Given:

Current in each wire: $I_1 = I_2 = 10\ \text{mA} = 10 \times 10^{-3}\ \text{A}$

Distance between wires: $r = 10\ \text{cm} = 0.1\ \text{m}$

Formula: Force per unit length between two parallel current-carrying conductors:

$\frac{F}{L} = \frac{\mu_0}{2\pi} \cdot \frac{I_1 I_2}{r}$

Substitute values:

$\frac{F}{L} = \frac{\mu_0}{2\pi} \cdot \frac{(10 \times 10^{-3})^2}{0.1}$

$\frac{F}{L} = \frac{\mu_0}{2\pi} \cdot \frac{100 \times 10^{-6}}{0.1}$

$\frac{F}{L} = \frac{\mu_0}{2\pi} \cdot 10^{-3}$