$A$ rectangular surface of sides $10 \,cm$ and $15 \,cm$ is placed inside a uniform electric field of $25 \,V/m$,such that the surface makes an angle of $30^{\circ}$ with the direction of the electric field. Find the flux of the electric field through the rectangular surface in $Nm^2/C$.

An infinitely long wire has a uniform linear charge density $\lambda = 2 \ nC/m$. The net flux through a Gaussian cube of side length $a = \sqrt{3} \ cm$, if the wire passes through any two corners of the cube that are maximally displaced from each other, would be $x \ Nm^2 C^{-1}$, where $x$ is: [Neglect any edge effects and use $\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \ SI$ units] (in $\pi$)

Five charges $+q, +5q, -2q, +3q$ and $-4q$ are situated as shown in the figure. The electric flux due to this configuration through the surface $S$ is

For a closed surface $\oint \vec{E} \cdot d\vec{s} = 0$,then:

An infinite line charge is at the axis of a cylinder of length $1 \,m$ and radius $7 \,cm$. If the electric field at any point on the curved surface of the cylinder is $250 \,NC^{-1}$,then the net electric flux through the cylinder is ............ $Nm^2C^{-1}$.

$A$ charge $q$ is located at the centre of a cube. The electric flux through any face is