Electric field at a point varies as $r^0$ for

Find the electric field due to an infinitely long charged cylinder of radius $R$ having a linear charge density $\lambda$ at a distance of $R/2$ from its axis.

$A$ non-conducting solid sphere has radius $R$ and uniform charge density. $A$ spherical cavity of radius $\frac{R}{4}$ is hollowed out of the sphere. The distance between the center of the sphere and the center of the cavity is $\frac{R}{2}$. If the charge of the sphere is $Q$ after the creation of the cavity and the magnitude of the electric field at the center of the cavity is $E = K \left( \frac{Q}{4 \pi \epsilon_0 R^2} \right)$,determine the approximate value of $K$.

Consider a sphere of radius $R$ which carries a uniform charge density $\rho$. If a sphere of radius $\frac{R}{2}$ is carved out of it,as shown,the ratio $\frac{|\overrightarrow{E}_{A}|}{|\overrightarrow{E}_{B}|}$ of the magnitude of the electric field $\overrightarrow{E}_{A}$ and $\overrightarrow{E}_{B}$ respectively,at points $A$ and $B$ due to the remaining portion is

The electric field intensity at $P$ and $Q$,in the shown arrangement,are in the ratio:

The electric field at a distance $R$ from the surface of a uniformly charged nonconducting sphere of radius $R$ is $20 \,V/m$. The electric field at a distance $\frac{R}{2}$ from the centre of the sphere is $.... \,V/m$.