Three equal charge Q are at the vertices of an equilateral triangle of side A. How much work is done (by an external angent ) in bringing them closser to an equilateral triangle of side A/2?

Explanation

To find the work done by an external agent in bringing three equal charges \( Q \) from the vertices of an equilateral triangle of side \( A \) to a new position where the side length is \( \frac{A}{2} \), we need to calculate the change in potential energy of the system.

### Step-by-Step Solution:

1. **Calculate the Initial Potential Energy (U_initial)**:
The potential energy \( U \) between two point charges \( Q_1 \) and \( Q_2 \) separated by a distance \( r \) is given by:
\[
U = k \frac{Q_1 Q_2}{r}
...