Show that the tangential component of electrostatic field is continuous from one side of charged surface to another. [Hint : use the fact that work done by electrostatic field on a closed – loop is zero.]

Explanation

To show that the tangential component of the electrostatic field is continuous across a charged surface, we can follow these steps:

### Step 1: Define the Electrostatic Field
Consider two regions separated by a charged surface. Let \( E_1 \) be the tangential component of the electric field just outside the surface (Region 1) and \( E_2 \) be the tangential component just inside the surface (Region 2).

### Step 2: Consider a Closed Loop
We can define a closed loop that consists of four points: A, B, C, and D. The path AB is in Region 1, BC is across the surface, CD is in Region 2, and DA returns to point A.

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