Four particles each having a charge q, are placed on the four vertices of a regular pentagon. The distance of each corner from the centre is a. Find the electric field at the centre of the pentagon.

Explanation

To find the electric field at the center of a regular pentagon with four charges placed at its vertices, we can follow these steps:

### Step 1: Understand the Configuration
We have a regular pentagon with four charges \( q \) located at its vertices. The distance from the center of the pentagon to each vertex is given as \( a \).

### Step 2: Electric Field Due to a Single Charge
The electric field \( E \) due to a single charge \( q \) at a distance \( a \) from the charge is given by the formula:
\[
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