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1. Show that the normal component of electrostatic field has a discontinuity from one side of a charged surface to another given by

$(\text{E}_2-\text{E}_1).\hat{\text{n}}=\frac{\sigma}{\in_0}$

where $\hat{\text{n}}$ is a unit vector normal to the surface at a point and σ is the surface charge density at that point. (The direction of $\hat{\text{n}}$ is from side 1 to side 2.) Hence show that just outside a conductor, the electric field is σ $\hat{\text{n}} /ε_0.$

2. 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.]