In bringing an electron towards another electron, the electrostatic potential energy of the system

Options

A. decreases
B. increases
C. remains same
D. becomes zero

Explanation

To solve the problem of the electrostatic potential energy of a system when bringing one electron towards another electron, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Charges**:
- We have two electrons, each with a charge of \( q = -1.6 \times 10^{-19} \) C.

2. **Understand the Interaction**:
- Since both charges are negative, they will repel each other due to the electrostatic force.

3. **Work Done Against Repulsion**:
- When bringing one electron closer to another, work must be done against this repulsive force. This work done is stored as electrostatic potential energy in the system.

4. **Formula for Electrostatic Potential Energy**:
- The electrostatic potential energy \( U \) of two point charges is given by the formula:
\[ U = \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r} \]
- Here, \( q_1 \) and \( q_2 \) are the charges, \( r \) is the distance between them, and \( \epsilon_0 \) is the permittivity of free space.

5. **Substituting Values**:
- For two electrons (where \( q_1 = q_2 = -1.6 \times 10^{-19} \) C), the formula becomes:
\[ U = \frac{1}{4 \pi \epsilon_0} \frac{(-1.6 \times 10^{-19})(-1.6 \times 10^{-19})}{r} = \frac{(1.6 \times 10^{-19})^2}{4 \pi \epsilon_0 r} \]

6. **Analyzing the Relationship**:
- The potential energy \( U \) is inversely proportional to \( r \). As \( r \) decreases (the electrons get closer), \( U \) increases.

7. **Conclusion**:
- Therefore, as we bring one electron closer to another, the electrostatic potential energy of the system increases.

### Final Answer:
The electrostatic potential energy of the system increases when bringing an electron towards another electron.

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