The electric field at $20 \,cm$ from the centre of a uniformly charged non-conducting sphere of radius $10 \,cm$ is $E$. Then at a distance $5 \,cm$ from the centre it will be

An infinitely long thin straight wire has a uniform linear charge density of $\frac{1}{3} \, C \cdot m^{-1}$. The magnitude of the electric field intensity at a point $18 \, cm$ away is (given $\varepsilon_0 = 8.85 \times 10^{-12} \, C^2 \cdot N^{-1} \cdot m^{-2}$):

The electric field inside a spherical shell of uniform surface charge density is

$A$ 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

$X$ and $Y$ are large,parallel conducting plates close to each other. Each face has an area $A$. $X$ is given a charge $Q$. $Y$ is without any charge. Points $A, B$,and $C$ are as shown in the figure.

Obtain the expression for the electric field due to:
$(i)$ An infinite plane sheet with uniform charge distribution.
$(ii)$ $A$ thin spherical shell with uniform charge distribution at a point outside it.
$(iii)$ $A$ thin spherical shell with uniform charge distribution at a point inside it.