$A$ point charge causes an electric flux of $-2 \times 10^4 \ Nm^2 C^{-1}$ to pass through a spherical Gaussian surface of $8.0 \ cm$ radius,centred on the charge. The value of the point charge is: (Given $\epsilon_0 = 8.85 \times 10^{-12} \ C^2 N^{-1} m^{-2}$)

If charge $q$ is placed on one of the vertex of a cube, then total electric flux passing through the cube is . . . . . . .

The figure shows electric field lines due to a charge configuration. From this,we conclude that:

If the electric field is given by $\vec{E} = (5 \hat{i} + 4 \hat{j} + 9 \hat{k})$. The electric flux through a surface of area $20$ units lying in the $Y-Z$ plane will be (in units):

If a charge $Q$ is placed at the corner of a cube,what is the electric flux passing through one of its faces?

An infinitely long uniform line charge distribution of charge per unit length $\lambda$ lies parallel to the $y$-axis in the $y-z$ plane at $z=\frac{\sqrt{3}}{2} a$ (see figure). If the magnitude of the flux of the electric field through the rectangular surface $A B C D$ lying in the $x-y$ plane with its center at the origin is $\frac{\lambda L }{ n \varepsilon_0}$ (where $\varepsilon_0$ is the permittivity of free space),then the value of $n$ is