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

Charges are uniformly spread on the surface of a conducting sphere. The electric field from the centre of the sphere to a point outside the sphere varies with distance $r$ from the centre as:

An electrostatic field in a region is radially outward with magnitude $E = \alpha r$,where $\alpha$ is a constant and $r$ is the radial distance. The charge contained in a sphere of radius $R$ in this region (centered at the origin) is:

Match List-$I$ with List-$II$:

List-$I$	List-$II$
$(A)$ Electric field inside (distance $r < R$ from center) of a uniformly charged spherical shell with surface charge density $\sigma$ and radius $R$.	$(I)$ $\sigma / \varepsilon_0$
$(B)$ Electric field at distance $r$ from a uniformly charged infinite plane sheet with surface charge density $\sigma$.	$(II)$ $\sigma / 2 \varepsilon_0$
$(C)$ Electric field outside (distance $r > R$ from center) of a uniformly charged spherical shell with surface charge density $\sigma$ and radius $R$.	$(III)$ $0$
$(D)$ Electric field between $2$ oppositely charged infinite plane parallel sheets with uniform surface charge density $\sigma$.	$(IV)$ $\frac{\sigma R^2}{\varepsilon_0 r^2}$

Choose the correct answer from the options given below:

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 $1 \,m$ from $S$ and has a speed of $1 \,m/s$. The maximum value of $\sigma$ if the electron strikes $S$ at $t=1 \,s$ is $\alpha \left[ \frac{m \epsilon_0}{e} \right] \,C/m^2$. The value of $\alpha$ is:

Obtain an expression for the electric field at the surface of a charged conductor.