A long cylindrical shell carries positive surface charge $\sigma$ in the upper half and negative surface charge $-\sigma$ in the lower half. The electric field lines around the cylinder will look like figure given in : (figures are schematic and not drawn to scale)

Four closed surfaces and corresponding charge distributions are shown below

Let the respective electric fluxes through the surfaces be ${\phi _1},{\phi _2},{\phi _3}$ and ${\phi _4}$ . Then

Figure shows four charges $q_1, q_2, q_3$ and $q_4$ fixed in space. Then the total flux of electric field through a closed surface $S$, due to all charges $q_1, q_2, q_3$ and $q_4$ is

An electric dipole is put in north-south direction in a sphere filled with water. Which statement is correct

$Assertion\,(A):$ A charge $q$ is placed on a height $h / 4$ above the centre of a square of side b. The flux associated with the square is independent of side length.

$Reason\,(R):$ Gauss's law is independent of size of the Gaussian surface.

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 ...... .