The horizontal component of earth's magnetic field at a place is $3.5 \times 10^{-5} \mathrm{~T}$. A very long straight conductor carrying current of $\sqrt{2} \mathrm{~A}$ in the direction from South east to North West is placed. The force per unit length experienced by the conductor is __________ $\times 10^{-6} \mathrm{~N} / \mathrm{m}$.