A uniform electric field exists in $x-y$ plane. The potential of points $A\left(-2m,2m\right),B\left(-2m,2m\right)$ and $C\left(2m,4m\right)$ are $4V,16V$ and 1$2V$ respectively. The electric field is

$(E_2-E_1)\dot{}\hat{n}\frac{\sigma }{{\epsilon }_0}$
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.]

(a) inside the sphere

(b) just outside the sphere