Four identical charges q are kept on each vertices of a square of side a. Calculate the extra amount of work done in bringing a Q charge from infinity to the centre of the square.

Explanation

To solve the problem of calculating the extra amount of work done in bringing a charge \( Q \) from infinity to the center of a square with four identical charges \( q \) at its vertices, we can follow these steps:

### Step 1: Understand the Configuration
We have a square with side length \( a \) and four identical charges \( q \) placed at each vertex. We need to find the work done in bringing a charge \( Q \) from infinity to the center of the square.

### Step 2: Determine the Potential at the Center
The potential \( V \) at a point due to a point charge is given by the formula:
\[
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