What is the electric field intensity at a point at a distance $r$ $(r < R)$ from the center of a charged spherical conductor of radius $R$ carrying a charge $Q$?

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 $\varepsilon_0 = 8.85 \times 10^{-12} \, C^2 \cdot N^{-1} \cdot m^{-2}$):

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 $\mu C/m$.

The electric field due to an infinitely long thin straight wire with uniform linear charge density of $2.5 \times 10^{-7} \ Cm^{-1}$ at a radial distance of $x$ from the wire is $7.5 \times 10^4 \ NC^{-1}$. Then $x=$ (in $cm$)

An infinite line of charge with uniform line charge density of $\lambda = 1 \ C \ m^{-1}$ is placed along the $y$-axis. $A$ point charge $q = 1 \ C$ is placed on the $x$-axis at a distance of $d = 3 \ m$ from the origin. At what distance $r$ from the origin on the $x$-axis,between the origin and the point charge,is the total electric field zero (in $m$)?

$A$ uniform rod $AB$ of mass $m$ and length $l$ is hinged at its midpoint $C$. The left half $(AC)$ of the rod has linear charge density $-\lambda$ and the right half $(CB)$ has $+\lambda$,where $\lambda$ is constant. $A$ large non-conducting sheet of uniform surface charge density $\sigma$ is also present near the rod. Initially,the rod is kept perpendicular to the sheet. The end $A$ of the rod is initially at a distance $d$. Now,the rod is rotated by a small angle $\theta$ in the plane of the paper and released. The time period of small angular oscillations is: