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

The space between two large parallel plates is filled with a material of uniform charge density $\rho$. Assume that one of the plates is kept at $x=0$. The potential at any point $x$ between these plates is given by (where $A$ and $B$ are constants):

Two long thin charged rods with charge density $\lambda$ each are placed parallel to each other at a distance $d$ apart. The force per unit length exerted on one rod by the other will be (where $k = \frac{1}{4 \pi \varepsilon_0}$)

The electric field near a conducting surface having a uniform surface charge density $\sigma$ is given by:

An infinitely long thin straight wire has a uniform linear charge density of $\frac{1}{3} \text{ C m}^{-1}$. The magnitude of the force acting on a charge of $3 \mu\text{C}$ situated at a point $18 \text{ cm}$ away from the wire is:
$\left(\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \text{ N m}^2 \text{ C}^{-2}\right)$

$A$ 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 $\epsilon_{0} = 8.85 \times 10^{-12} \ C^{2} \ N^{-1} \ m^{-2}$]