A linear charge having linear charge density $\lambda$ , penetrates a cube diagonally and then it penetrate a sphere diametrically as shown. What will be the ratio of flux coming cut of cube and sphere

Each of two large conducting parallel plates has one sided surface area $A$. If one of the plates is given a charge $Q$ whereas the other is neutral, then the electric field at a point in between the plates is given by

Gauss’s law is true only if force due to a charge varies as

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

Gauss’s law should be invalid if

A cubical volume is bounded by the surfaces $x =0, x = a , y =0, y = a , z =0, z = a$. The electric field in the region is given by $\overrightarrow{ E }= E _0 \times \hat{ i }$. Where $E _0=4 \times 10^4 NC ^{-1} m ^{-1}$. If $a =2 cm$, the charge contained in the cubical volume is $Q \times 10^{-14} C$. The value of $Q$ is $...........$

Take $\left.\varepsilon_0=9 \times 10^{-12} C ^2 / Nm ^2\right)$