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?

At a distance $l$ from a uniformly charged long wire, a charged particle is thrown radially outward with a velocity $u$ in the direction perpendicular to the wire. When the particle reaches a distance $2l$ from the wire, its speed is found to be $\sqrt{2}u$. The magnitude of the velocity, when it is a distance $4l$ away from the wire is (ignore gravity)

An infinite line charge produces a field of $9 \times 10^4 \; N/C$ at a distance of $2 \; cm$. Calculate the linear charge density in $\mu C/m$.

$A$ very long charged solid cylinder of radius 'a' contains a uniform charge density $\rho$. The dielectric constant of the material of the cylinder is $k$. What will be the magnitude of the electric field at a radial distance '$x$' $(x < a)$ from the axis of the cylinder?

$A$ spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is

Two infinite parallel metal planes contain electric charges with charge densities $+\sigma$ and $-\sigma$ respectively, and they are separated by a small distance in air. If the permittivity of air is $\varepsilon_{0}$, then the magnitude of the field between the two planes with its direction will be: