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

How does the electric field lines depend on area ?

The flat base of a hemisphere of radius $a$ with no charge inside it lies in a horizontal plane. A uniform electric field $\vec E$ is applied at an angle $\frac {\pi }{4}$ with the vertical direction. The electric flux through the curved surface of the hemisphere is

Choose the incorrect statement :

$(a)$ The electric lines of force entering into a Gaussian surface provide negative flux.

$(b)$ A charge ' $q$ ' is placed at the centre of a cube. The flux through all the faces will be the same.

$(c)$ In a uniform electric field net flux through a closed Gaussian surface containing no net charge, is zero.

$(d)$ When electric field is parallel to a Gaussian surface, it provides a finite non-zero flux.

Choose the most appropriate answer from the options given below

If an electric field is given by $10 \hat{i}+3 \hat{j}+4 \hat{k}$, calculate the electric flux through a surface of area $10$ units lying in $y z$ plane ....... units

A disk of radius $a / 4$ having a uniformly distributed charge $6 C$ is placed in the $x-y$ plane with its centre at $(-a / 2,0,0)$. A rod of length $a$ carrying a uniformly distributed charge $8 C$ is placed on the $x$-axis from $x=a / 4$ to $x=5 a / 4$. Two point charges $-7 C$ and $3 C$ are placed at $(a / 4,-$ $a / 4,0)$ and $(-3 a / 4,3 a / 4,0)$, respectively. Consider a cubical surface formed by six surfaces $x=\pm a / 2, y=\pm a / 2, z=\pm a / 2$. The electric flux through this cubical surface is