An infinite nonconducting sheet of charge has a surface charge density of $10^{-7} \ C/m^2$. The separation between two equipotential surfaces near the sheet whose potential differ by $5 \ V$ is:

$A$ charged ball $B$ hangs from a silk thread $S,$ which makes an angle $\theta$ with a large charged conducting sheet $P,$ as shown in the figure. The surface charge density $\sigma$ of the sheet is proportional to $:-$

What is the electric field intensity at a point at a distance $r$ $(r < R)$ from the center of a charged spherical conductor of radius $R$ carrying a charge $Q$?

In the figure,the inner (shaded) region $A$ represents a sphere of radius $r_A=1$,within which the electrostatic charge density varies with the radial distance $r$ from the center as $\rho_A=k r$,where $k$ is positive. In the spherical shell $B$ of outer radius $r_B$,the electrostatic charge density varies as $\rho_B=\frac{2 k}{r}$. Assume that dimensions are taken care of. All physical quantities are in their $SI$ units. Which of the following statement$(s)$ is(are) correct?

Three infinitely long charged non-conducting sheets are placed as shown in the figure. The electric field at point $P$ is ($\sigma$ - charge density,$\epsilon_0$ - permittivity of free space).

$A$ particle of charge $-q$ and mass $m$ moves in a circle of radius $r$ around an infinitely long line charge of linear density $+\lambda$. Then the time period will be given as (Consider $k$ as Coulomb's constant).