Which of the following statements are correct?

(a) The density of electric lines of force at a point is independent of the magnitude of electric field intensity vector $E$ at that point.
(b) The density of electric lines of force at a point is proportional to the magnitude of electric field intensity vector $E$ at that point.
(c) Actually, the electric field lines do not exist. This is just a graphical description of the electric field.
(d) Actually, the electric field lines exist.

Electric field is given by $\overrightarrow{E}=\left(8\hat{\mathrm{i}}+4\hat{\mathrm{j}}+3\hat{\mathrm{k}}\right) \mathrm{N} {\mathrm{C}}^{-1}$. Electric flux through surfaces of area $100 {\mathrm{m}}^2$ layer in $X\mathit{-}Y$ plane, $Y-Z$ plane and $X-Z$ plane are in ratio

A conic surface is placed in a uniform electric field $E$ as shown in the figure such that the field is perpendicular to the surface on the side $AB$. The base of the cone is of the radius $R$, and the height of the cone is $h$. The angle of the cone is $\mathrm{\theta }$. Find the magnitude of the flux that enters the cone’s curved surface from the left side. Do not count the outgoing flux $\left(\mathrm{\theta }<45°\right)$.

The figure below shows an imaginary cube of side $a.$ A uniformly charged rod of length $\frac{a}{2}$ moves towards the right at a constant speed $v.$ At $t=0,$ the right end of the rod just touches the left face of the cube. Plot a graph between electric flux $\left({\varphi }_{\mathrm{E}}\right)$ passing through the cube versus time $\left(t\right)$.

A graph of the $x$ component of the electric field as a function of $x$ in a region of space is shown. The $y$ and $z$ components of the electric field are zero in this region. If the electric potential is $10 \mathrm{V}$ at the origin, then the potential at $x=2.0 \mathrm{m}$ is