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 placed along $x-$axis in $X - Y$ plane. There is a point $P$ located between the conductors (as shown in figure). <Br> A charge particle of $3\pi $ coulomb is passing through the point $P$ with velocity $\vec v = \left( {2\hat i + 3\hat j} \right)\,\,m/s;$ where $\hat i\,\,and\,\,\hat j$ represents unit vector along $x\,\,\& \,\,y$ axis respectively. <Br> The force acting on the charge particle is $4\pi \times {10^{ - 5}}\left( { - x\hat i + 2\hat j} \right)N.$ The value of $x$ is: <Br>