A non-conducting solid sphere of radius $R$ is uniformly charged. The magnitude of the electric field due to the sphere at a distance $r$ from its centre

The electric field $\vec E = {E_0}y\hat j$ acts in the space in which a cylinder of radius $r$ and length $l$ is placed with its axis parallel to $y-$ axis. The charge inside the volume of cylinder is 

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

Let $\rho (r) =\frac{Q}{{\pi {R^4}}}r$ be the charge density distribution for a solid sphere of radius $R$ and total charge $Q$. For a point '$p$' inside the sphere at distance $r_1$ from the centre of the sphere, the magnitude of electric field is

Three infinitely long charged thin sheets are placed as shown in figure. The magnitude of electric field at the point $P$ is $\frac{x \sigma}{\epsilon_0}$. The value of $x$ is_____. (all quantities are measured in $SI$ units).

A solid metal sphere of radius $R$ having charge $q$ is enclosed inside the concentric spherical shell of inner radius $a$ and outer radius $b$ as shown in figure. The approximate variation electric field $\overrightarrow{{E}}$ as a function of distance $r$ from centre $O$ is given by