An infinitely long line charge having linear charge density $\lambda$ lies at a distance $d$ from center of an imaginary sphere of radius $R$. Then

A charge $q$ is placed at one corner of a cube as shown in figure. The flux of electrostatic field $\overrightarrow{E}$ through the shaded area 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 an 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:

A cube is placed inside an electric field, $\overrightarrow{E}=150y^2\hat{\mathrm{j}}$ The side of the cube is $0.5 \mathrm{m}$ and is placed in the field as shown in the given figure. The charge inside the cube is:

A point charge of $+12 \mu \mathrm{C}$ is at a distance $6 \mathrm{cm}$ vertically above the centre of a square of side $12 \mathrm{cm}$ as shown in figure. The magnitude of the electric flux through the square will be _________ $\times {10}^3 \mathrm{N} {\mathrm{m}}^2 {\mathrm{C}}^{-1}.$(Write the value to the nearest integer)

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 $ABCD$ ?

A charge $q$ sits at the black corner of a cube as shown in the following figure:

What is the electric flux through the shaded side?

The black shapes in the figure below are closed surfaces. The electric field lines are in red. For which case, the net flux through the surfaces is non-zero?

A point electric charge $Q$ is placed at a corner of a cube as shown in the figure. What is the electric flux passing through $ABCD$ of the cube? (${\in }_0$ is permittivity of free space)