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

If the electric field is given by $\vec{E} = (5 \hat{i} + 4 \hat{j} + 9 \hat{k})$. The electric flux through a surface of area $20$ units lying in the $Y-Z$ plane will be (in units):

What is the net flux of the uniform electric field of $E = 3 \times 10^{3} \hat{i} \; N/C$ through a cube of side $20 \; cm$ oriented so that its faces are parallel to the coordinate planes?

Two co-axial conducting cylinders of same length $\ell$ with radii $\sqrt{2} R$ and $2 R$ are kept,as shown in Fig. $1$. The charge on the inner cylinder is $Q$ and the outer cylinder is grounded. The annular region between the cylinders is filled with a material of dielectric constant $\kappa=5$. Consider an imaginary plane of the same length $\ell$ at a distance $R$ from the common axis of the cylinders. This plane is parallel to the axis of the cylinders. The cross-sectional view of this arrangement is shown in Fig. $2$. Ignoring edge effects,the flux of the electric field through the plane is ($\epsilon_0$ is the permittivity of free space):

$A$ point charge $+10 \; \mu C$ is at a distance $5 \; cm$ directly above the centre of a square of side $10 \; cm$,as shown in the figure. What is the magnitude of the electric flux through the square?

How does the number of electric field lines depend on the area?