Eight point charges , each `q` , are placed on the vertices of a cube of side `a`. Find the potential energy of the system of charges.

Explanation

To find the potential energy of a system of eight point charges, each of charge \( q \), placed at the vertices of a cube with side length \( a \), we can follow these steps:

### Step 1: Determine the number of unique pairs of charges
The total number of unique pairs of charges can be calculated using the combination formula \( \binom{n}{2} \), where \( n \) is the number of charges. For 8 charges, the number of pairs is:
\[ \text{Number of pairs} = \binom{8}{2} = \frac{8 \times 7}{2} = 28 \]

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