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 charges \( q_1 \) and \( q_3 \).

### Step-by-Step Solution:

1. **Understanding the Initial Force**:
The force exerted by charge \( q_1 \) on charge \( q_2 \) is given by Coulomb's Law:
\[ F_{12} = \frac{k \cdot |q_1 \cdot q_2|}{r^2} \]
where \( k = \frac{1}{4 \pi \epsilon_0} \) is Coulomb's constant, and \( r \) is the distance between \( q_1 \) and \( q_2 \).

**Hint**: Recall that the force between two charges is dependent on the product of their magnitudes and inversely proportional to the square of the distance between them.

2. **Introducing a Third Charge**:
When a third charge \( q_3 \) is brought near \( q_2 \), it will exert a force on \( q_2 \) as well. The force exerted by \( q_3 \) on \( q_2 \) can be expressed as:
\[ F_{32} = \frac{k \cdot |q_3 \cdot q_2|}{d^2} \]
where \( d \) is the distance between \( q_3 \) and \( q_2 \).

**Hint**: Remember that the force exerted by \( q_3 \) on \( q_2 \) depends on the magnitude of \( q_3 \) and its distance from \( q_2 \).

3. **Net Force on \( q_2 \)**:
The net force acting on \( q_2 \) is the vector sum of the forces due to \( q_1 \) and \( q_3 \):
\[ F_{net} = F_{12} + F_{32} \]
This indicates that the net force on \( q_2 \) will change due to the presence of \( q_3 \).

**Hint**: Consider that the net force is the sum of all forces acting on a charge, and it can change even if one of the forces remains constant.

4. **Effect of \( q_3 \) on \( F_{12} \)**:
It is important to note that the introduction of \( q_3 \) does not affect the force \( F_{12} \) (the force between \( q_1 \) and \( q_2 \)). The force \( F_{12} \) remains:
\[ F_{12} = \frac{k \cdot |q_1 \cdot q_2|}{r^2} \]
unchanged, regardless of the presence of \( q_3 \).

**Hint**: The force between two charges is only influenced by those two charges and their distance; other charges nearby do not alter this specific interaction.

5. **Conclusion**:
Therefore, the force exerted by \( q_1 \) on \( q_2 \) remains the same even after bringing \( q_3 \) near \( q_2 \).

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