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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

$(\text{E}_2-\text{E}_1).\hat{\text{n}}=\frac{\sigma}{\epsilon_0}$
where $\hat{\text{n}}$ is a unit vector normal to the surface at a point and $\sigma$ is the surface charge density at that point. $ ($The direction of $\hat{\text{n}}$ is from side $1$ to side $2.)$ Hence show that just outside a conductor, the electric field is $\sigma \hat{\text{n}} /ε_0.$

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.$]$