When the separation between two charges is increased, the electric potential energy of the charges

Options

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

Answer

To solve the question regarding how the electric potential energy of two charges changes when their separation is increased, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Electric Potential Energy**:
The electric potential energy (U) between two point charges \( Q_1 \) and \( Q_2 \) separated by a distance \( R \) is given by the formula:
\[ U = \frac{k \cdot Q_1 \cdot Q_2}{R} \]
where \( k \) is Coulomb's constant.

2. **Analyzing the Effect of Increasing Distance**:
- If the charges \( Q_1 \) and \( Q_2 \) are of the **same sign** (both positive or both negative), the potential energy \( U \) is **positive**. As the distance \( R \) increases, the value of \( U \) decreases because \( U \) is inversely proportional to \( R \):
\[ U \propto \frac{1}{R} \]
Thus, increasing \( R \) leads to a decrease in potential energy.

3. **Considering Opposite Charges**:
- If the charges \( Q_1 \) and \( Q_2 \) are of **opposite signs** (one positive and one negative), the potential energy \( U \) is **negative**. In this case, as the distance \( R \) increases, the potential energy \( U \) becomes less negative (or increases towards zero):
\[ U \propto -\frac{1}{R} \]
Therefore, increasing \( R \) leads to an increase in potential energy.

4. **Conclusion**:
- For **like charges** (same sign), increasing the separation decreases the potential energy.
- For **unlike charges** (opposite signs), increasing the separation increases the potential energy.
- Therefore, the change in electric potential energy depends on the nature of the charges.

### Final Answer:
When the separation between two charges is increased, the electric potential energy of the charges:
- Decreases if the charges are of the same sign.
- Increases if the charges are of opposite signs.