Short Answer 
The electrostatic potential energy of a system with three charges can be calculated using a specific formula that incorporates the charges and their distances. By substituting the given values into the formula and evaluating it, the result indicates a negative potential energy of -1.42 x 10^-5 joules, suggesting a bound state of the charges.
Step 1: Understand the Formula
The electrostatic potential energy of a system of charges can be calculated using the formula: U = frac{1}{4pi epsilon_0} left( frac{q_1q_2}{r_{12}} + frac{q_1q_3}{r_{13}} + frac{q_2q_3}{r_{23}} right). This formula takes into account three pairs of charges (q1, q2, and q3) and their distances (r12, r13, r23). Understanding each term is crucial for accurate calculations.
Step 2: Substitute Given Values
Using the following given values, plug them into the formula:
- q1 = -15 µC
- q2 = 10 µC
- q3 = 16 µC
- r12 = 3 cm = 0.03 m
- r13 = 5 cm = 0.05 m
- r23 = 4 cm = 0.04 m
Step 3: Calculate the Result
Evaluate the calculations step-by-step: combine the terms and substitute the value of epsilon_0 = 8.85 times 10^{-12}. The final calculation leads to: U = -1.42 times 10^{-5} joules, indicating that the electrostatic potential energy of the system is negative, which shows a bound state of the charges.