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
Answer & explanation
Correct answer: option 1
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:
$\frac{F}{L} = \frac{\mu_0}{2\pi} \cdot \frac{(10 \times 10^{-3})^2}{0.1}$
$\frac{F}{L} = \frac{\mu_0}{2\pi} \cdot \frac{100 \times 10^{-6}}{0.1}$
$\frac{F}{L} = \frac{\mu_0}{2\pi} \cdot 10^{-3}$
= $10 × 10^{-4} (μ_0/2π) N/m$