A system consists of two thin concentric metal shells of radii `R_(1)` and `R_(2)` with corresponding charges `q_(1)` and `q_(2)`. Find the selfenergy values `W_(1)` and `W_(2)` of each shell, the interaction energy of the shells `W_(12)`, and the total electric energy of the system.

Explanation

To solve the problem, we need to find the self-energy values \( W_1 \) and \( W_2 \) for each shell, the interaction energy \( W_{12} \) between the shells, and the total electric energy of the system.

### Step 1: Calculate the Self-Energy of Shell 1 (\( W_1 \))

The self-energy of a charged shell can be calculated using the formula:

\[
W_1 = \frac{1}{2} \frac{q_1^2}{R_1}
...