Physics - Magnetism Question with Solution | TestHub

Two long parallel conductors $S_1$ and $S_2$ are separated by a distance $10 \mathrm{cm}$ and carrying currents of $4 \mathrm{A}$ and $2 \mathrm{A}$ 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).
A charge particle of $3\pi$ coulomb is passing through the point $P$ with velocity $\overrightarrow{v}=\left(2\hat{i}+3\hat{j}\right) \mathrm{m} {\mathrm{s}}^{-1}$; where $\hat{i}$ & $\hat{j}$ represents unit vector along $x$ & $y$axis respectively.
The force acting on the charge particle is $4\pi \times {10}^{-5}\left(-x\hat{i}+2\hat{j}\right) \mathrm{N}$. The value of $x$ is