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 Problem
Consider a charged surface that separates two different media, Medium 1 and Medium 2. We denote the tangential components of the electric field in Medium 1 and Medium 2 as \( E_{t1} \) and \( E_{t2} \), respectively.

### Step 2: Construct a Closed Loop
To analyze the electric field, we will consider a closed loop that straddles the charged surface. This loop will have a small width, denoted as \( \Delta x \), and will extend into both media.

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