Two long parallel wires separated by a distance of 2.50 cm, repel each other with a force of $4 × 10^{-5} N/m$. The current in one wire is 0.5 A. The current in the second wire will be

10 A

The correct answer is Option (2) → 10 A

Force per unit length between two parallel currents: $F/L = \frac{\mu_0 I_1 I_2}{2\pi d}$

Given: $F/L = 4\times10^{-5}\ \text{N/m}$, $I_1 = 0.5\ \text{A}$, $d = 2.5\ \text{cm} = 0.025\ \text{m}$, $\mu_0 = 4\pi \times 10^{-7}\ \text{T·m/A}$

$I_2 = \frac{2 \pi d (F/L)}{\mu_0 I_1} = \frac{2 \pi (0.025) (4\times10^{-5})}{4 \pi \times 10^{-7} \cdot 0.5}$

$I_2 = \frac{6.2832\times10^{-6}}{6.2832\times10^{-7}} = 10\ \text{A}$

Current in the second wire = 10 A