The electric field in a region is uniform and is given by $\vec{E} = a \hat{i} + b \hat{j} + c \hat{k}$. The electric flux associated with a surface of area $\vec{A} = \pi R^2 \hat{i}$ is:

$A$ point charge $+q$ is placed in front of a grounded metal plate. Points $P$ and $Q$ are between the charge $X$ and the plate $Y$ as shown in the figure. Let $E_P$ and $E_Q$ be the magnitudes of the electric fields at points $P$ and $Q$ respectively. Which of the following statements is true?

$A$ charged body has an electric flux $\phi$ associated with it. The body is now placed inside a metallic container. The flux $\phi$ outside the container will be

$A$ charged shell of radius $R$ carries a total charge $Q$. Let $\Phi$ be the flux of the electric field through a closed cylindrical surface of height $h$,radius $r$,with its center coinciding with that of the shell. The center of the cylinder is a point on the axis of the cylinder equidistant from its top and bottom surfaces. Which of the following option$(s)$ is/are correct? [$\epsilon_0$ is the permittivity of free space]
$(1)$ If $h > 2R$ and $r > R$,then $\Phi = \frac{Q}{\epsilon_0}$
$(2)$ If $h < \frac{8R}{5}$ and $r = \frac{3R}{5}$,then $\Phi = 0$
$(3)$ If $h > 2R$ and $r = \frac{4R}{5}$,then $\Phi = \frac{2Q}{5\epsilon_0}$
$(4)$ If $h > 2R$ and $r = \frac{3R}{5}$,then $\Phi = \frac{Q}{5\epsilon_0}$

$A$ spherical rubber balloon carries a charge,uniformly distributed over its surface. As the balloon is blown up and increases in size,the total electric flux coming out of the surface

$A$ point charge $q$ is placed at the corner of a cube of side $a$ as shown in the figure. What is the electric flux through the face $ABCD$?