Deduce an expression for the potential energy of a system of two point charges `q_1` and `q_2` located at positions `r_1` and `r_2` respectively in an external field `(vecE)`

Explanation

To deduce the expression for the potential energy of a system of two point charges \( q_1 \) and \( q_2 \) located at positions \( \vec{r}_1 \) and \( \vec{r}_2 \) respectively in an external electric field \( \vec{E} \), we can follow these steps:

### Step 1: Understanding the System
We have two point charges \( q_1 \) and \( q_2 \) positioned at \( \vec{r}_1 \) and \( \vec{r}_2 \) in an external electric field \( \vec{E} \). The potential energy of the system will be influenced by both the external electric field and the interaction between the two charges.

### Step 2: Work Done in Bringing the Charges
To find the potential energy, we need to consider the work done in bringing each charge from infinity to its respective position in the electric field.

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