In a cuboid of dimension $2 \mathrm{~L} \times 2 \mathrm{~L} \times \mathrm{L}$, a charge $q$ is placed at the centre of the surface ' $S$ ' having area of $4 \mathrm{~L}^2$. The flux through the opposite surface to ' $\mathrm{S}$ ' is given by

• A

  $\frac{\mathrm{q}}{12 \varepsilon_0}$
• B

  $\frac{\mathrm{q}}{3 \varepsilon_0}$
• C

  $\frac{\mathrm{q}}{2 \varepsilon_0}$
• Correct answer
  D

  $\frac{q}{6 \varepsilon_0}$

Solution

After placing similar cubic at the bottom, we get cube of side $2 \mathrm{~L}$ having change $\mathrm{q}$ at its centre.

From the Gauss's law electric flux through whole


Flux passing through shaded face
$\phi=\frac{\mathrm{q} / \varepsilon_0}{6}=\frac{\mathrm{q}}{6 \varepsilon_0}$

Hence, the correct answer is option: 'D'.