A charge is distributed uniformly over a ring of radius ‘a’. Obtain an expression for the electric intensity E at a point on the axis of the ring. Hence show that for points at large distances from the ring, it behaves like a point charge.

Explanation

To solve the problem of finding the electric intensity \( E \) at a point on the axis of a uniformly charged ring, we will follow these steps:

### Step 1: Understand the Configuration
Consider a ring of radius \( a \) with a uniform charge \( Q \) distributed over it. Let \( P \) be a point on the axis of the ring at a distance \( x \) from the center of the ring.

### Step 2: Define Linear Charge Density
Let \( \lambda \) be the linear charge density of the ring, given by:
\[
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