$A$ charge $Q$ is placed at the center of a cube. The total electric flux passing through all six faces of the cube is ..........

In the figure,a $+Q$ charge is located at one of the corners of the cube. What is the electric flux through the cube due to the $+Q$ charge?

$A$ point charge $+Q$ is placed just outside an imaginary hemispherical surface of radius $R$ as shown in the figure. Which of the following statements is/are correct?
$[A]$ The electric flux passing through the curved surface of the hemisphere is $-\frac{Q}{2 \varepsilon_0}\left(1-\frac{1}{\sqrt{2}}\right)$
$[B]$ Total flux through the curved and the flat surfaces is $\frac{Q}{\varepsilon_0}$
$[C]$ The component of the electric field normal to the flat surface is constant over the surface
$[D]$ The circumference of the flat surface is an equipotential

$A$ square surface of side $L$ meters is in the plane of the paper. $A$ uniform electric field $\vec{E} \text{ (V/m)}$ is also in the plane of the paper,limited only to the lower half of the square surface. The electric flux associated with the surface in $SI$ units is:

It is not convenient to use a spherical Gaussian surface to find the electric field due to an electric dipole using Gauss's theorem because

$(a)$ An electrostatic field line is a continuous curve. That is,a field line cannot have sudden breaks. Why not?
$(b)$ Explain why two field lines never cross each other at any point?