Three identical point charges q are kept on each vertices of an equilateral triangle of side a. Calculate the work done in slowly moving the charges to the mid points of each side, covering the shortest possible distance.

Explanation

To solve the problem of calculating the work done in slowly moving three identical point charges \( q \) from the vertices of an equilateral triangle to the midpoints of each side, we can follow these steps:

### Step 1: Initial Configuration
We start with three identical point charges \( q \) placed at the vertices of an equilateral triangle with side length \( a \). The potential energy \( U_i \) of the system can be calculated using the formula for the potential energy of point charges:

\[ U_i = k \left( \frac{q^2}{a} + \frac{q^2}{a} + \frac{q^2}{a} \right) = 3 \frac{k q^2}{a} \]
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