Question

Charge in the form of a plane sheet with density $\sigma =40\mu {\text{C/m}}^2$ is located at $z=–0.5\text{m}$. A uniform line of charge of density $\lambda =-6\mu \text{C/m}$ lies along the $y-$ axis. Net flux that crosses the surface of cube $2\text{m}$ as an edge, centered at the origin as shown, is $K\frac{{10}^{-6}}{{\epsilon }_0}\frac{N}{C}{m}^2$. Then value of $K$ is

Answer 1

Total charge enclosed inside the cube
$q_{en}=(40\times 4-6\times 2)\mu \text{C}=(160-12)\mu \text{C}$
$q_{en}=148\mu \text{C}$
Net flux that crosses the surface of the cube,
$\frac{q_{en}}{{\epsilon }_0}=148\times \frac{{10}^{-6}}{{\epsilon }_0}\frac{N}{C}{m}^2$
$K=148$