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 ________$\times {10}^{-6} \mathrm{N} {\mathrm{m}}^{-1}$.