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

Explanation

To solve the problem of how much work is 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 Initial Potential Energy
The potential energy \( U_i \) of the system of charges when they are at the vertices of an equilateral triangle of side \( A \) can be calculated using the formula for potential energy between two point charges:

\[ U_i = k \left( \frac{Q^2}{A} + \frac{Q^2}{A} + \frac{Q^2}{A} \right) \]
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