An $100 \ eV$ electron is fired directly towards a large metal plate having surface charge density $-2 \times 10^{-6} \ C \ m^{-2}$. The distance from where the electron is projected,so that it just fails to strike the plate,is: (in $mm$)

Consider a long uniformly charged cylinder having constant volume charge density $\rho$ and radius $R$. $A$ Gaussian surface is in the form of a cylinder of radius $r$ such that the vertical axis of both cylinders coincide. For a point inside the cylinder $(r < R)$,the electric field is directly proportional to

$A$ 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):

The volume charge density in a spherical ball of radius $R$ varies with distance $r$ from the centre as $\rho(r)=\rho_0\left[1-\left(\frac{r}{R}\right)^3\right]$,where $\rho_0$ is a constant. The radius at which the electric field would be maximum is

$A$ conducting sphere of radius $R = 20 \ cm$ is given a charge $Q = 16 \ \mu C$. What is the electric field $\overrightarrow{E}$ at the centre?

At a point $20\, cm$ from the centre of a uniformly charged dielectric sphere of radius $10\, cm$, the electric field is $100\, V/m$. The electric field at $3\, cm$ from the centre of the sphere will be.......$V/m$.