The adjoining diagram shows the electric lines of force emerging from a charged body. If the electric fields at $A$ and $B$ are $E_A$ and $E_B$ respectively and the distance between them is $r$,then

$A$ point charge of $2.0 \; \mu C$ is at the centre of a cubic Gaussian surface $9.0 \; cm$ on edge. What is the net electric flux through the surface?

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,the net flux through a closed Gaussian surface containing no net charge is zero.
$(d)$ When the 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:

$A$ 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 ..........

Consider an electric field $\vec{E} = E_0 \hat{i}$,where $E_0$ is a constant. The flux through the shaded area (as shown in the figure) due to this field is

$A$ charge $Q$ is enclosed by a Gaussian surface of radius $R$. If the radius is doubled,then the outward electric flux will