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 $\mu C / m$

Obtain the expression of electric field by ……

$(i)$ infinite size and with uniform charge distribution.

$(ii)$ thin spherical shell with uniform charge distribution at a point outside it.

$(iii)$ thin spherical shell with uniform charge distribution at a point inside it.

A spherical conductor of radius $12 \;cm$ has a charge of $1.6 \times 10^{-7} \;C$ distributed uniformly on its surface. What is the electric field

$(a)$ inside the sphere

$(b)$ just outside the sphere

$(c)$ at a point $18\; cm$ from the centre of the sphere?

The volume charge density of a sphere of radius $6 \,m$ is $2 \,\mu cm ^{-3}$. The number of lines of force per unit surface area coming out from the surface of the sphere is $….\times 10^{10}\, NC ^{-1}$.  [Given : Permittivity of vacuum  $\left.\epsilon_{0}=8.85 \times 10^{-12} C ^{2} N ^{-1}- m ^{-2}\right]$

Let $\sigma$ be the uniform surface charge density of two infinite thin plane sheets shown in figure. Then the electric fields in three different region $E_{ I }, E_{ II }$ and $E_{III}$ are