As shown in the figure,a ball $B$ is suspended by a string $S$ from a large charged plate $P$ such that it makes an angle $\theta$ with the plate. The surface charge density of the plate is proportional to which of the following?

$A$ 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).

Two large thin parallel metal plates have surface charge densities of equal magnitude but opposite signs $(\sigma = 26.4 \times 10^{-12} \ C/m^2)$. The electric field between these plates is ........ $N/C$.

Let $\sigma$ be the uniform surface charge density of two infinite thin plane sheets shown in the figure. Then the electric fields in three different regions $I, II$ and $III$ are:

An infinitely long solid cylinder of radius $R$ has a uniform volume charge density $\rho$. It has a spherical cavity of radius $R/2$ with its centre on the axis of the cylinder,as shown in the figure. The magnitude of the electric field at the point $P$,which is at a distance $2R$ from the axis of the cylinder,is given by the expression $\frac{23\rho R}{16K\varepsilon_0}$. The value of $K$ is

$A$ solid metallic sphere has a charge $+3Q$. Concentric with this sphere is a conducting spherical shell having charge $-Q$. The radius of the sphere is $a$ and that of the spherical shell is $b$ $(b > a)$. What is the electric field at a distance $R$ $(a < R < b)$ from the center?