Show that the normal component of electrostatic field has a discontinuity from one side of a charged surface to another given by `(E_(2)-E_(1)).hatn=sigma/epsi_(0)` where `hatn` is a unit vector normal to the surface at a point and `sigma` is the surface charge density at that point. (The direction of `hatn` is from side 1 to side 2). Hence show that just outside a conductor, the electric field is `(sigma hatn)/(epsi_(0))`.
(b) Show that the tangetial component of electrostatic field field is continuous from one side of a charged surface to another. [Hint: For (a), use Gauss law. For (b) use the fact that work done by electrostatic field on a a closed loop is zero].