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

Answer

To solve the problem of how the electrostatic potential energy changes when bringing an electron towards another electron, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Electrostatic Potential Energy**:
The electrostatic potential energy (U) between two point charges is given by the formula:
\[ U = \frac{k \cdot q_1 \cdot q_2}{r} \]
where \( k \) is Coulomb's constant, \( q_1 \) and \( q_2 \) are the charges, and \( r \) is the distance between the charges.

2. **Identifying Charges and Distances**:
In this case, both charges are electrons, so:
\[ q_1 = q_2 = -e \]
where \( e \) is the magnitude of the charge of an electron. Initially, the distance between the two electrons is \( r_1 \).

3. **Calculating Initial Potential Energy**:
The initial potential energy \( U_i \) when the distance is \( r_1 \) is:
\[ U_i = \frac{k \cdot (-e) \cdot (-e)}{r_1} = \frac{k \cdot e^2}{r_1} \]

4. **Bringing the Electron Closer**:
When we bring one electron closer to the other, the new distance becomes \( r_2 \) (where \( r_2 < r_1 \)).

5. **Calculating Final Potential Energy**:
The final potential energy \( U_f \) at distance \( r_2 \) is:
\[ U_f = \frac{k \cdot (-e) \cdot (-e)}{r_2} = \frac{k \cdot e^2}{r_2} \]

6. **Comparing Initial and Final Potential Energies**:
Since \( r_2 < r_1 \), we know that:
\[ \frac{1}{r_2} > \frac{1}{r_1} \]
Therefore, \( U_f > U_i \).

7. **Calculating Change in Potential Energy**:
The change in potential energy \( \Delta U \) is given by:
\[ \Delta U = U_f - U_i \]
Since \( U_f > U_i \), it follows that:
\[ \Delta U > 0 \]
This indicates that the potential energy of the system increases when bringing the electron closer.

8. **Conclusion**:
Thus, the electrostatic potential energy of the system increases when an electron is brought closer to another electron.

### Final Answer:
The electrostatic potential energy of the system **increases**.