$A$ point charge $q$ is placed at the corner of a cube of side $a$ as shown in the figure. What is the electric flux through the face $ABCD$?

The electric field in a region of space is given by $\overrightarrow E = E_0 \hat i + 2E_0 \hat j$,where $E_0 = 100 \, N/C$. The flux of the field through a circular surface of radius $0.02 \, m$ parallel to the $Y-Z$ plane is nearly:

$A$ long straight wire of radius $1 \, mm$ has a uniform charge distribution. The charge per $cm$ length of the wire is $Q \, Coulombs$. $A$ cylinder of radius $50 \, cm$ and length $1 \, m$ encloses the wire symmetrically. The total flux passing through the surface of the cylinder is ..........

$A$ point charge causes an electrical flux of $-1.0 \times 10^3 \ Nm^2 \ C^{-1}$ to pass through a spherical Gaussian surface of $10 \ cm$ radius centered on the charge. If the radius of the Gaussian surface were $3$ times,how much flux would pass through the surface?

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 $\pi$)

Consider the charges and the Gaussian surface shown in the figure. When calculating the electric flux through the spherical surface,the electric field is due to which of the following?