For an infinite line of charge having charge density $\lambda$ lying along the $x$-axis,the work required in moving a charge $q$ from point $C$ to point $A$ along the arc $CA$ is:

$A$ spherical shell with an inner radius $a$ and an outer radius $b$ is made of conducting material. $A$ point charge $+Q$ is placed at the centre of the spherical shell and a total charge $-q$ is placed on the shell. Find the final charge distribution on the surfaces.

$A$ solid sphere of radius $r_1=1 \text{ cm}$ carries charge distributed uniformly over it with density $\rho_1=-3 \text{ C/cm}^3$. It is surrounded by a concentric spherical shell of radius $r_2=2 \text{ cm}$ carrying uniform charge density $\rho_2=0.5 \text{ C/cm}^3$. If $E_d$ denotes the magnitude of the electric field at distance $d$ from the common centre of the spheres,then

$A$ 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 potential due to an electrostatic charge distribution is $V(r) = \frac{q e^{-\alpha r}}{4 \pi \varepsilon_{0} r}$,where $\alpha$ is positive. The net charge within a sphere centred at the origin and of radius $1/\alpha$ is

$A$ negatively charged plate has a surface charge density of $\sigma = 2 \times 10^{-6} \ C/m^2$. An electron with kinetic energy $KE = 200 \ eV$ is projected towards the plate. If the electron does not strike the plate,find the minimum initial distance $r$ in $mm$ from the plate.