Consider a parallel plate capacitor of $10\mu F$ (micro-farad) with air filled in the gap between the plates. Now one half of the space between the plates is filled with a dielectric of dielectric constant $4$, as shown in the figure. The capacity of the capacitor charges to

$(E_2-E_1)\dot{}\hat{n}\frac{\sigma }{{\epsilon }_0}$
where $\hat{n}$ is a unit vector normal to the surface at a point and $\sigma$ is the surface charge density at that point. (The direction of $\hat{n}$ is from side 1 to side 2.) Hence show that just outside a conductor, the electric field is $\sigma \hat{n}/{ϵ}_0$
(b) Show that the tangential component of electrostatic field is continuous from one side of a charged surface to another.  [Hint: For (a), use Gauss's law. For, (b) use the fact that work done by electrostatic field on a closed loop is zero.]