An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet $S$ having surface charge density $+\sigma$. The electron at $t=0$ is at a distance of $1 \mathrm{~m}$ from $S$ and has a speed of $1 \mathrm{~m} / \mathrm{s}$. The maximum value of $\sigma$ if the electron strikes $S$ at $t=1 \mathrm{~s}$ is $\alpha\left[\frac{\mathrm{m} \in_0}{\mathrm{e}}\right] \frac{\mathrm{C}}{\mathrm{m}^2}$ the value of $\alpha$ is

If an insulated non-conducting sphere of radius $R$ has charge density $\rho $. The electric field at a distance $r$ from the centre of sphere $(r < R)$ will be

An infinitely long solid cylinder of radius $R$ has a uniform volume charge density $\rho$. It has a spherical cavity of radius $R / 2$ with its centre on the axis of the cylinder, as shown in the figure. The magnitude of the electric field at the point $P$, which is at a distance $2 \ R$ from the axis of the cylinder, is given by the expression $\frac{23 \rho R }{16 k \varepsilon_0}$. The value of $k$ is

Which of the following graphs shows the variation of electric field $E$ due to a hollow spherical conductor of radius $R$ as a function of distance $r$ from the centre of the sphere

Graphical variation of electric field due to a uniformly charged insulating solid sphere of radius $R$, with distance $r$ from the centre $O$ is represented by:

An isolated sphere of radius $R$ contains uniform volume distribution of positive charge. Which of the curve shown below, correctly illustrates the dependence of the magnitude of the electric field of the sphere as a function of the distance $r$ from its centre?