A quarter ring of radius `R` is having uniform charge density `lambda`. Find the electric field and potential at the centre of the ring.

Explanation

To solve the problem of finding the electric field and potential at the center of a quarter ring with radius \( R \) and uniform charge density \( \lambda \), we can follow these steps:

### Step 1: Understanding the Configuration
We have a quarter ring that subtends an angle of \( 90^\circ \) (or \( \frac{\pi}{2} \) radians) at the center. The charge density is uniform, denoted as \( \lambda \).

### Step 2: Consider a Small Charge Element
Let’s consider a small charge element \( dq \) on the quarter ring. The length of this small charge element can be expressed as:
\[
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