Electric flux through a surface of area $100 \ m^2$ lying in the $xy$ plane is (in $V-m$) if $\vec E = \hat i + \sqrt 2 \hat j + \sqrt 3 \hat k$.

$q_1, q_2, q_3$ and $q_4$ are point charges located at points as shown in the figure and $S$ is a spherical Gaussian surface of radius $R$. Which of the following is true according to Gauss's law?

$A$ disk of radius $a/4$ having a uniformly distributed charge $6 \text{ C}$ 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 $8 \text{ C}$ is placed on the $x$-axis from $x = a/4$ to $x = 5a/4$. Two point charges $-7 \text{ C}$ and $3 \text{ C}$ are placed at $(a/4, -a/4, 0)$ and $(-3a/4, 3a/4, 0)$,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

Which among the curves shown in the figure cannot possibly represent electrostatic field lines?

In a uniform electric field,a cube of side $1 \ cm$ is placed. The total energy stored in the cube is $8.85 \ \mu J$. The electric field is parallel to four of the faces of the cube. The electric flux through any one of the remaining two faces is

Consider an electric field $\vec{E} = 3 \times 10^3 \hat{i} \text{ N/C}$. What is the flux through a square of side $10 \text{ cm}$ in $Nm^2/C$ if the normal to its plane makes a $60^\circ$ angle with the $X$-axis?