An electron is projected, as shown in the figure, with kinetic energy $K$ and at an angle $\text{θ}=45°$ between the two charged plates. What should be the magnitude of the electric field between the plates so that the electron just fails to strike the upper charged plate?

$4 \times 10^{10}$ electrons are removed from a neutral metal sphere of diameter $20 \mathrm{cm}$ placed in air. The magnitude of the electric field (in $\mathrm{N} {\mathrm{C}}^{-1}$ ) at a distance of $20 \mathrm{cm}$ from its centre is

The figure below shows field lines of an electric field. The spacing between the lines parallel to the page is same everywhere. If the magnitude of the field at $A$ is $40 \mathrm{N} {\mathrm{C}}^{-1}$, then the magnitude of the field at $B$ is approximately,

A long cylindrical shell carries positive surface charge $\sigma$ in the upper half and negative surface charge $-\sigma$ in the lower half. The electric field lines around the cylinder will look like figure given in: (figures are schematic and not drawn to scale)

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