A charge `q_(1)` exerts some force on a second charge `q_(2)` If a third charge `q_(3)` is brought near `q_(2)`, then the force exterted by `q_(1)` on `q_(2)`

Options

A. decrease
B. increase
C. remains the same
D. increase, if `q_(3)` is of same sign as `q_(1)` and decrease, if `q_(3)` is of opposite sign as `q_(1)`

Answer

To solve the problem, we need to analyze the forces acting on charge \( q_2 \) due to the presence of charges \( q_1 \) and \( q_3 \).

### Step-by-step Solution:

1. **Identify the Charges and Their Interactions**:
- We have three charges: \( q_1 \), \( q_2 \), and \( q_3 \).
- The force exerted by \( q_1 \) on \( q_2 \) is given by Coulomb's law.

2. **Coulomb's Law**:
- According to Coulomb's law, the force \( F \) between two point charges is given by:
\[ F = k \frac{|q_1 q_2|}{r^2} \]
- Here, \( k \) is Coulomb's constant, \( r \) is the distance between the charges, and the force is directed along the line joining the two charges.

3. **Force Exerted by \( q_1 \) on \( q_2 \)**:
- The force exerted by \( q_1 \) on \( q_2 \) (let's call it \( F_{12} \)) is independent of any other charges present. It solely depends on the magnitudes of \( q_1 \) and \( q_2 \) and the distance \( r \) between them.

4. **Introducing the Third Charge \( q_3 \)**:
- When we bring a third charge \( q_3 \) near \( q_2 \), it will exert its own force on \( q_2 \) (let's call this force \( F_{32} \)).
- The presence of \( q_3 \) does not change the force \( F_{12} \) exerted by \( q_1 \) on \( q_2 \).

5. **Conclusion**:
- The force exerted by \( q_1 \) on \( q_2 \) remains the same regardless of the presence of \( q_3 \). Therefore, the correct answer is that the force exerted by \( q_1 \) on \( q_2 \) remains the same.

### Final Answer:
**The force exerted by \( q_1 \) on \( q_2 \) remains the same.**