Three infinitely long charge sheets are placed as shown in the figure. The electric field at point $P$ is

The electric field in a region is radially outward and at a point is given by $E = 250 r \, V/m$ (where $r$ is the distance of the point from the origin). Calculate the charge contained in a sphere of radius $20 \, cm$ centered at the origin in Coulombs $(C)$.

$A$ cube of side $a$ is placed in an electric field $\vec{E} = E_0 x \hat{i}$. What is the total charge enclosed by the cube?

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 $mm$)

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

Consider an atom with atomic number $Z$ as consisting of a positive point charge at the centre and surrounded by a distribution of negative electricity uniformly distributed within a sphere of radius $R$. The electric field at a point inside the atom at a distance $r$ from the centre is