What is the flux through a cube of side $a$ if a point charge of $q$ is at one of its corners?

Obtain the expression for the electric field due to a uniformly charged spherical shell at a point outside it.

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

Explain by graph how the electric field by a thin spherical shell depends on the distance of a point from the centre.

$A$ sphere of radius $R$ has a volume charge density $\rho = k r$, where $r$ is the distance from the center of the sphere and $k$ is a constant. The magnitude of the electric field at the surface of the sphere is given by ($\varepsilon_{0} =$ permittivity of free space):

$A$ large metal plate has a surface charge density of $8.85 \times 10^{-6} \ C \ m^{-2}$. An electron having initial kinetic energy of $8 \times 10^{-17} \ J$ is moving towards the center of the plate. If the electron stops just before reaching the plate,then the initial distance between the electron and the plate is [Take $\epsilon_{0} = 8.85 \times 10^{-12} \ C^{2} \ N^{-1} \ m^{-2}$]