When the separation between two charges is increase the electric potential energy of the charges.

Options

A. increases
B. decreases
C. remains the same.
D. may increase or decrease

Explanation

To solve the question regarding the effect of increasing the separation between two charges on their electric potential energy, we can follow these steps:

### Step 1: Understand Electric Potential Energy Formula
The electric potential energy (U) between two point charges \( Q \) and \( q \) separated by a distance \( R \) is given by the formula:
\[ U = \frac{k \cdot Q \cdot q}{R} \]
where \( k \) is Coulomb's constant.

### Step 2: Analyze the Effect of Increasing Distance
When the separation \( R \) between the two charges is increased, we need to analyze how it affects the potential energy \( U \).

- If \( R \) increases, the denominator in the formula increases.
- Since \( k \), \( Q \), and \( q \) are constants, an increase in \( R \) will lead to a decrease in \( U \) if both charges are of the same sign (like charges).

### Step 3: Consider the Sign of Charges
The behavior of the potential energy also depends on the nature of the charges:
- **Like Charges (Both Positive or Both Negative)**:
- Here, \( U \) is positive. As \( R \) increases, \( U \) decreases.
- **Unlike Charges (One Positive and One Negative)**:
- Here, \( U \) is negative. As \( R \) increases, the absolute value of \( U \) decreases, which means \( U \) becomes less negative (i.e., increases).

### Step 4: Conclusion
Thus, when the separation between two charges is increased:
- For like charges, the electric potential energy decreases.
- For unlike charges, the electric potential energy increases.

### Final Answer
The electric potential energy of the charges may either increase or decrease depending on whether the charges are like or unlike.

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