Draw the electric field lines of a positive point charge.

Select the correct statement$(s)$:
$(1)$ The density of electric field lines is independent of the magnitude of the electric field vector $E$ at a given point.
$(2)$ The density of electric field lines is proportional to the magnitude of the electric field vector $E$ at a given point.
$(3)$ Electric field lines do not exist in reality. They are only a graphical representation of the electric field.
$(4)$ Electric field lines exist in reality.

What kind of Gaussian surface is used to calculate the electric field due to the charge distribution?

In the figure,a point charge $+Q_1$ is at the centre of an imaginary spherical surface and another point charge $+Q_2$ is outside it. Point $P$ is on the surface of the sphere. Let $\Phi _s$ be the net electric flux through the sphere and $\vec E_p$ be the electric field at point $P$ on the sphere. Which of the following statements is $TRUE$?

$A$ point charge causes an electric flux of $-1.0 \times 10^{3} \; N \cdot m^{2} / C$ to pass through a spherical Gaussian surface of $10.0 \; cm$ radius centered on the charge.
$(a)$ If the radius of the Gaussian surface were doubled,how much flux would pass through the surface?
$(b)$ What is the value of the point charge?

$A$ wire has a charge of $Q \text{ coulomb}$ per $cm$. What is the total electric flux passing through the cylinder of length $1 \ m$?