$A$ cylinder of radius $R$ and length $L$ is placed in a uniform electric field $E$ parallel to the cylinder axis. The total flux for the surface of the cylinder is given by-

Consider a cylinder of length $L$ and radius $R$ placed in a uniform electric field $E$ such that its axis is parallel to the electric field. The total electric flux associated with the cylinder is .......

$A$ square loop of sides $a=1 \ m$ is held normally in front of a point charge $q=1 \ C$. The charge is placed at a distance of $a/2$ from the center of the square. The flux of the electric field through the shaded region is $\frac{5}{p} \times \frac{1}{\varepsilon_0} \frac{N m^2}{C}$,where the value of $p$ is . . . . . . .

If the radius of the spherical Gaussian surface is increased,then the electric flux due to a point charge enclosed by the surface:

If $\vec E = \frac{E_0 x}{a} \hat i$,then find the electric flux through the shaded area of the cube as shown in the figure,where the shaded face is at $x = a$.

$A$ hemispherical surface of radius $a$ is placed in a uniform electric field $E$ such that the flat surface makes an angle of $\pi /4$ with the vertical. There is no charge inside the hemisphere. The electric flux passing through the curved surface of the hemisphere is: