Two long parallel conductors S _ 1 and S _ 2 are separated by a...

Net magnetic field at $P$ is {B}_{Net} = \left(\dfrac{{\mu}_{0} \times {i}_{1}}{2\pi{r}_{1}} - \dfrac{{\mu}_{0}{i}_{2}}{2\pi{r}_{2}}\right)\left(- \overset{^}{k}\right)

${B}_{Net} = \dfrac{{\mu}_{0}4}{2\pi \times \dfrac{4}{100}} - \dfrac{{\mu}_{0}2}{2\pi \times \dfrac{6}{100}}$

$= \dfrac{{\mu}_{0}}{\pi} \times 100\left[\dfrac{1}{2} - \dfrac{1}{6}\right]$

$= \dfrac{{\mu}_{0}}{\pi} \times 100\left[\dfrac{4}{2 \times 6}\right]$

= \dfrac{{\mu}_{0} \times 100}{3\pi}\left(- \overset{^}{k}\right)

So, force acting on charge particle is\overset{\to}{F} = q\left(\overset{\to}{v} \times \overset{\to}{B}\right) = 3\pi\left[2\overset{^}{i} + 3\overset{^}{j}\right]\dfrac{{\mu}_{0} \times 100}{3\pi}\left(- \overset{^}{k}\right)

= 4\pi \times {10}^{- 7}\left[2\overset{^}{i} + 3\overset{^}{j}\right] \times 100\left(- \overset{^}{k}\right)

= 4\pi \times {10}^{- 5}\left[2\overset{^}{j} - 3\overset{^}{i}\right]

$∴ x = 3$