(a) 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)).n = sigma/epsilon_(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 //epsilon_(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.]