Two long parallel conductors S_1 and S_2 are separated by a distance 10 cm and carrying currents of 4 A and 2 A respectively. The conductors are…

Two long parallel conductors $\displaystyle \mathrm{S}_1$ and $\displaystyle \mathrm{S}_2$ are separated by a distance $\displaystyle 10$ cm and carrying currents of $\displaystyle 4$ A and $\displaystyle 2$ A respectively. The conductors are placed along $\displaystyle x-$ axis in X-Y plane. There is a point P located between the conductors (as shown in figure). A charge particle of $\displaystyle 3 \pi$ coulomb is passing through the point P with velocity $\displaystyle \vec{v}=(2 \hat{i}+3 \hat{j}) \mathrm{m} / \mathrm{s}$; where $\displaystyle \hat{i} \& \hat{j}$ represents unit vector along $\displaystyle x \& y$ axis respectively. The force acting on the charge particle is $\displaystyle 4 \pi \times 10^{-5}(-x \hat{i}+2 \hat{j}) N$. The value of $\displaystyle x$ is: