Eight point charges of magnitude Q are arranged to form the corners of a cube of side L. The arrangement is made in manner such that the nearest neighbour of any charge has the opposite sign. Initially, the charges are held at rest. If the system is let free to move, what happens to the arrangement? Does the cube-shape shrink or expand? Calculate the velocity ct each charge when the side-length of the cube formation changes from L to nL. Assume that the mass of each point charge is m.

Explanation

To solve the problem, we need to analyze the arrangement of the charges and the potential energy associated with them. Here’s a step-by-step breakdown:

### Step 1: Understanding the Configuration
We have 8 point charges of magnitude \( Q \) at the corners of a cube of side length \( L \). The arrangement is such that each charge has a nearest neighbor with an opposite sign. This means we have alternating charges at the corners of the cube.

### Step 2: Calculate the Potential Energy
The potential energy \( U \) of the system can be calculated by considering the interactions between the charges.

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