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 solve the problem of calculating 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 equilateral triangle of side \( \frac{A}{2} \), we will follow these steps:

### Step 1: Calculate the Initial Potential Energy

The potential energy \( U_i \) of a system of point charges is given by the formula:

\[
U = k \sum_{i < j} \frac{q_i q_j}{r_{ij}}
...