An infinite line of charge with linear density of charge, $\lambda =2\times {10}^{-6} \mathrm{C}/\mathrm{m}$ exists. Calculate the electrostatic force on a point charge of $5.0 \mathrm{mC}$ at a distance of $50 \mathrm{cm}$ from the line of charge.

Using Gauss law, derive expression for electric field due to a spherical shell of uniform charge distribution $\sigma$ and radius $R$ at a point lying at a distance $x$ from the centre of shell, such that $0<x<R$.

Using Gauss law, derive expression for electric field due to a spherical shell of uniform charge distribution $\sigma$ and radius $R$ at a point lying at a distance $x$ from the centre of shell, such that $x>R$.

State Gauss's law in electrostatics and write in its mathematical form.Calculate the electric field $\overrightarrow{\mathrm{E}}$ at point $\mathrm{P}$ due to charges this spherical shell, shown in figure (1) What will be the field $\overrightarrow{E}$ shown in fig (2) and (3)? Given the surface charge density is $\sigma$.

Find an expression for the electric field intensity due to a uniformly charged thin spherical shell at a point outside the shell.