$A$ charge of $1 \,C$ is located at the centre of a sphere of radius $10 \,cm$ and a cube of side $20 \,cm$. The ratio of outgoing flux from the sphere and cube will be

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

The electric field in a region is given by $\vec{E}=(2 \hat{i}+4 \hat{j}+6 \hat{k}) \times 10^3 \ N/C$. The flux of the field through a rectangular surface parallel to the $x-z$ plane is $6.0 \ N m^2 C^{-1}$. The area of the surface is . . . . . . $cm^2$.

The dimensional formula for electric flux is $..........$

If the electric flux entering and leaving an enclosed surface respectively is ${\varphi _1}$ and ${\varphi _2}$,the electric charge inside the surface will be:

$A$ 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?