# 2.16 (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.]

Let's assume a Rectangular loop of length l and small width b.

Now,

Line integral along the loop :

$\oint E.dl=E_1l-E_2l=0$

This implies

$E_1cos\theta_1l-E_2cos\theta_2l=0$

From here,

$E_1cos\theta_1=E_2cos\theta_2$

Since $E_1cos\theta_1$ and $E_2cos\theta_2$ are the tangential component of the electric field, the tangential component of the electric field is continuous across the surface

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