$A$ point charge $q$ is placed on the center of the flat circular base of a hemispherical surface as shown in the figure. The net flux of the electric field through the hemispherical surface is closest to:

An infinitely long thin non-conducting wire is parallel to the $z$-axis and carries a uniform line charge density $\lambda$. It pierces a thin non-conducting spherical shell of radius $R$ in such a way that the arc $PQ$ subtends an angle $120^{\circ}$ at the centre $O$ of the spherical shell,as shown in the figure. The permittivity of free space is $\epsilon_0$. Which of the following statements is (are) true?
$(A)$ The electric flux through the shell is $\sqrt{3} R \lambda / \epsilon_0$
$(B)$ The $z$-component of the electric field is zero at all the points on the surface of the shell
$(C)$ The electric flux through the shell is $\sqrt{2} R \lambda / \epsilon_0$
$(D)$ The electric field is normal to the surface of the shell at all points

An electric field $\overrightarrow{E} = (2x\hat{i}) \text{ NC}^{-1}$ exists in space. $A$ cube of side $2 \text{ m}$ is placed in the space as per the figure given below. The electric flux through the cube is .................. $\text{Nm}^2 \text{C}^{-1}$.

Consider the integral form of the Gaussian law in electrostatics: $\oint \vec{E} \cdot d\vec{s} = \frac{Q}{\epsilon_0}$. Which of the following statements are correct?

$A$ point charge '$Q$' is placed at a point inside a hollow conducting sphere. Which of the following electric field patterns is correct?

Consider four closed surfaces $S_1, S_2, S_3,$ and $S_4$ each enclosing the same charge $q_1$. Compare the electric flux through these surfaces.